My 9 year old, high mileage car died suddenly and will cost more to repair than it would have been worth on trade-in if it was running, so I need to buy a used car this week. My two previous car loans were captive financing of new cars with FICO scores in the 700s, so this is my first time buying a car under less-than-great credit score circumstances and without a large down payment/trade in. It's a lot more stressful than before.
As of today, my FICO 8 scores are 639 EQ/642 TU/643 EXP, with FICO Auto 8 scores at 651 EQ/649 TU/672 EXP. The reason the scores are so low is that I happen to have very high utilization at the moment (87%) due to having to replace our home's heating system mid-winter (long story) and repairs to my husband's car. We had just started an aggressive debt payoff plan last month and then this happened to throw a wrench into those plans. 
No lates, but it looks like I have one small ($120) medical debt in collections from 2013. I didn't know this until I pulled my credit report yesterday, because I haven't needed to apply for credit since 2012 when we refinanced our mortgage - I know it's hurting my scores but I won't have a chance to address it before I need to get financed (in the next 2 days). I'm chalking that up to an expensive lesson learned. 
We only have $2000-2200 available for a down payment and unfortunately I don't expect to get much of anything for trade-in value out of the car with the blown engine. On the plus side, my salary is $94K/year and I've been at my job for over 14 years. My current DTI (mortgage, student loan, minimums on all revolving lines) is 25% and with the maximum car payment we'd be comfortable with right now, my DTI would be up to a maximum of 30%.
I went ahead and did the Capital One Auto Navigator pre-qualification (the dealership where I serviced the car with the blown engine participates). To my surprise given my mediocre scores, they pre-qualified me with APRs ranging from 3.89-5.03%, depending on which vehicle I'm modeling. Are these APRs legit? Also, the pre-qual letter doesn't say how much I can borrow - am I likely to get the $18-20K loan that I'd like, or should I prepare myself to maybe end up needing to choose a less-expensive car?
Anyone who's had positive or negative experiences with the Capital One pre-qual, I'd love to hear about it. I figure that if nothing else, it makes a handy negotiating tool.
Log in to the Capital One Autonavigator website they user your last name, zip and last 4 of ssn to login. there should be more details there on your prequalification. But from everything I have seen on here the rates are usually solid. it'll depend on the car, but you can build a deal right on the website and search for cars in their dealer network. To give you a better idea of overall cost and payment. Rate will change with amount down and term.
I used to work in the car industry. We would never contact the insurance company unless all the paperwork and financing is good. Not worth the effort faxing stuff. (yes insurance companies still use fax for some reason) YMMV but from my point of view it looks like you are in the clear.
If Cap1 pre-quals you, you're good to go. The only wrench in the works will be when they do the hard pull. If there's been a negative change to your reports since the pre-qual, the rate may go up on the offer. On the flip side, if you have positive changes, the rate may go down.
I know in Massachusetts atleast dealers need to get an RMV-1 form stamped by someone at the insurance agency to be able to register the car at all. So common practice was when getting the car ready to fax the insurance company with all of the deal information including the lien holder etc and an RMV-1 form filled out without the stamp and signature and we would get that back and hand in all the documents to our on site registry to either get plates or the new registration. Not sure where the OP lives but in MA this is common place as insurance is required to operate a vehichle in MA.