Applying for credit cards

[Anthony S.]

Having gone without credit cards for the past 5 years - following a bankruptcy - I need to obtain a couple credit cards in order to facilitate bidding on foreclosure auctions.  According to Credit Karma my credit score is presently 718, but the automated applications reject me immediately (applied to AmEx tonight) & I suspect it's because of the bankruptcy.

1.  Can I negatively affect my credit score by applying for - & being rejected for - too many credit cards in a given period?  (I just learned of the 5/24 rule.)

2.  What is the best way to obtain a credit card given the negative info on my report?

3. Will online foreclosure auctions tie-up credit on a credit card (i.e. $2,500 bidding authorizations)?

  3 a. If so, isn't that a good reason for getting as much credit as possible on each credit card one has?

Thanks,

ALS