if that card reports on your credit a maxed or near maxed card will hurt your credit.
Theres a lot of factors. What did they said was the denial reason? Have you pull your actual reports? When I first started, my report had much of maxed out CC reporting that wasn't mind. I kept getting denial until I correct it.
They would not tell me over the phone. I was told to wait till I got my letter in the mail. I have read that some ppl have called after getting the letter and have gotten them to change there minds. Also discover and capitol one send me stuff all the time should I go with one of them or will they Stoll deny the pre screen approved?
Yes, some creditors won't tell you over the phone. Wait until you get the letter and you better be able to explain the reasons they denied you. For example, if they said high utilization (most likely in your case), tell them that you're an AU on your mom's account and you don't use it anymore and show them that you always make on time payment on the other account with them.
For your second question, yes, you're more likely to get approved if they sent you offers, but not guaranty. I said go for the discover because they are trying to recruit new members for their IT card.