Fidelity is processed by Elan bank or US bank. They normally pull TU but will also pull one of the lesser known CRs not EX or EQ. They are the most conservative of those you've listed IME.
Penfed has always been strictly a EQ puller for me and most people reporting DPs.
Citi loves EX but does double pull EX and EQ sometimes on new customers. Same with Chase. Depending on the part of the country you live in. They'll pull EX and EQ or EX and TU. Some of the folks in California on the site, claim they only pulled EX for them.
I've done several in a day or several over a week. I made sure I did it before any of them reported the new accounts.
If you want some of those 5/24 Chase CCs. Grab those before any accounts report.
I'd hit Fidelity first. Followed by Penfed. It's a toss up on Citi and Chase. There's a good chance they'll both pull EX. Being the other two don't normally hit EX. That's still only two INQs on EX.
US bank has a soft pull prequal site. Doing the prequal may give you advanced warning on your chance of an approval.
You can also try Chase's prequal and Citi's pre-qualified site. All are normally solid offers. If you get a set APR, there's a higher chance of approval.
I've never had a prequal offer from Chase. So it doesn't mean you won't be approved, if you don't see any offers.
Penfed has always been strictly a EQ puller for me and most people reporting DPs.
Citi loves EX but does double pull EX and EQ sometimes on new customers. Same with Chase. Depending on the part of the country you live in. They'll pull EX and EQ or EX and TU. Some of the folks in California on the site, claim they only pulled EX for them.
I've done several in a day or several over a week. I made sure I did it before any of them reported the new accounts.
If you want some of those 5/24 Chase CCs. Grab those before any accounts report.
I'd hit Fidelity first. Followed by Penfed. It's a toss up on Citi and Chase. There's a good chance they'll both pull EX. Being the other two don't normally hit EX. That's still only two INQs on EX.
US bank has a soft pull prequal site. Doing the prequal may give you advanced warning on your chance of an approval.
You can also try Chase's prequal and Citi's pre-qualified site. All are normally solid offers. If you get a set APR, there's a higher chance of approval.
I've never had a prequal offer from Chase. So it doesn't mean you won't be approved, if you don't see any offers.
You can Google "credit pulls database". I used it as a reference until I built my own from apping.
Penfed is a terrific CU. The pull will be good for at least 30 days. In some cases they'll use it up to 90 days. So even if you went back to them weeks later and decided they had another product you wanted. They'll use the pull on file.
Citi is one of the favorites used here. They don't normally give massive limits from the start. It will grow with patience and using the SPs every 180 days to bump up the limit.
Penfed is a good CU to have in your corner. They can be VERY generous!
The 2% card does require a checking account to get the full 2%.
You use the same pull for everything with them.
Vantage West is another I wouldn't over look. The 5% card they have gives some fantastic rewards. I want that one myself.
Oh forgot to mention, you can only be approved for two Chase cards in a 30 day period. Anything over that will result in an automatic denial.
Penfed is a terrific CU. The pull will be good for at least 30 days. In some cases they'll use it up to 90 days. So even if you went back to them weeks later and decided they had another product you wanted. They'll use the pull on file.
Citi is one of the favorites used here. They don't normally give massive limits from the start. It will grow with patience and using the SPs every 180 days to bump up the limit.
Penfed is a good CU to have in your corner. They can be VERY generous!
The 2% card does require a checking account to get the full 2%.
You use the same pull for everything with them.
Vantage West is another I wouldn't over look. The 5% card they have gives some fantastic rewards. I want that one myself.
Oh forgot to mention, you can only be approved for two Chase cards in a 30 day period. Anything over that will result in an automatic denial.
As for why people go on app sprees.. lol I'd actually like to know how it really breaks down over time myself, app spree vs going slow, I can't speak for other's reasoning behind it but my own [quite possibly faulty] logic behind it is mainly a) hopefully get approved for multiple cards before the rest show up on your credit reports and drop your AAoA and possibly score along with it - I think this effect is a lot more pronounced the shorter your history is though and mine is very short, I think I've seen @ABCD2199 mention this before? He'd probably be able to help you figure out how much it would affect you personally if you were curious, you may have already encountered him but if not seriously this guy is a fico wizard and super helpful - anyway in the same vein as AAoA I figure there's also the whole CCC's not liking lots of new accounts thing, which as long as you plan out who is most likely to do their HP where then the amount of inquiries they can see should be a bit (or maybe even quite a bit) less than the actual number of cards you app'd for.. I wouldn't be the best example here since I don't have very many cards but I did get them all in the past 8 or 9 months and I did manage to get it so that I've only got 2 inq's per bureau.. it would be less if not for the notorious capital one triple pull 
but ideally that's what you'd try to do, requires a little research and planning, especially if you're going on a larger spree, and you'd probably also want to plan on the order to app in based on who has certain quirks - i.e. chase 5/24, if they're on your list you'd probably wanna go for theirs first - also might be pretty helpful to google credit pulls databases, but make sure you're not looking too far back to where the info is no longer valid.. you could also search for 'who does *lender/card* pull' to help plan things)
As for b), for me it would be to let the accounts age together, if they were all cards I was going to get anyway then I figure I may as well let them all age now vs one now and the rest later, since once you get to a point say 2 years down the road instead of having a few 2 year old cards you'd have one 2 year old card and a couple brand new ones.. but my logic here could be missing something, I'm definitely curious to know if any of this is even correct lol so I wouldn't really follow my example haha I'd definitely wait to hear from some other people on this (I do believe certain lenders get spooked if they see a ton of new accounts all pop up in a super short period, so that's one potential app spree downfall, i feel like I've seen it mentioned the most with people getting a bunch of shopping cart trick cards from the same lender though [i.e. synchrony and their notorious blue envelope, lol I saw that referenced around here so many times I had to google it] so it might not really apply to this scenario anyway)
But that's my logic behind it, possibly accurate or just as likely totally wrong haha but hopefully someone else will help out here 
Edit: whoops I forgot to hit post earlier and it looks like this has now been addressed haha but good to see I'm not totally off base on my points 
(Oh yeah also imo the 2 most helpful/popular credit pulls databases I've found are whogavemecredit and the credit boards credit pull database, in case you're googling them and aren't sure which ones to check out first)
I find no real value in the CSP. But I don't travel like that either. The only value I see in it is churning the bonus, the initial CL and being able to transfer the limit to another Chase card. Before the first year is up, I'd PC it to a Freedom and/or move the limit elsewhere.
That's the reason for grabbing two of their cards at once. Chase isn't big on CLIs for most of us. And they HP for requesting an increase. Which isn't guaranteed.
With two of the cards, you have options to move limits around without any additional pulls. Let's say in the future you find another Chase card useful but the SL is lower than what you need. You take some credit limits from one or more of your other Chase cards and make the limit what you want it to be. No HP CLI request needed.
By PCing you keep your account history without having to close the account entirely. And you avoid paying the AF. So you're not trapped at all.😉
There's no set number for an app spree. It depends on how old and thick your file is. Your score will dip a little for the first couple of months and then the points will return.
My scores were in the mid 600s when I began apping just over 2 1/2 years ago. I've had at least 50 new accounts in that period of time. I'm still in the mid to upper 700s. Getting four of the cards you want isn't going to send you into purgatory. lol
That's the reason for grabbing two of their cards at once. Chase isn't big on CLIs for most of us. And they HP for requesting an increase. Which isn't guaranteed.
With two of the cards, you have options to move limits around without any additional pulls. Let's say in the future you find another Chase card useful but the SL is lower than what you need. You take some credit limits from one or more of your other Chase cards and make the limit what you want it to be. No HP CLI request needed.
By PCing you keep your account history without having to close the account entirely. And you avoid paying the AF. So you're not trapped at all.😉
There's no set number for an app spree. It depends on how old and thick your file is. Your score will dip a little for the first couple of months and then the points will return.
My scores were in the mid 600s when I began apping just over 2 1/2 years ago. I've had at least 50 new accounts in that period of time. I'm still in the mid to upper 700s. Getting four of the cards you want isn't going to send you into purgatory. lol