Equifax shows the number of searches (what they do when you apply for credit), and I think they recommended this to be a maximum of 3 in every 6 month period so yod be better off leaving it a while before applying for credit. Not sure if they do this just to open a bank account tho?
6 or 7 late payment will go against you quite badly but I think only stays on your history for 6 years after the debt was settled. 6 years is a long time you will get it cleared eventually if you keep up to date with future payments.
Once your credit rating gets better, try n get a small overdraft but dont use it as such. Just it being there will improve your score