The one from 7/11 is not affecting your score anymore. The other inquiries are likely having a fairly minor effect, maybe 10 points or a little more. I don't think it's going to be a big deal. Certainly not a dealbreaker as far as getting approved. Hard to say whether you might be near an interest break cutoff. What might have more of an effect is when the two new Amex cards start reporting. Are they your first Amex cards? If so, you're going to get dinged for two new accounts and the resulting lowering of your AAoA. Not sure by how much though. Depends on what's on your reports.
What's on your other reports. The lender you go to might not even use EX. Also, they are going to use an auto-enhanced score. Do you have prior auto history?
Starting Score: ~500 (12/01/2008)