Usual disclaimer: I am not an expert; this is not financial advice; it is my opinion & you take it or leave it at your own risk.

1) The simple fact of having 3 credit cards does not preclude getting more; I currently have 5, of which 2 have ongoing balances. You do, however, need to limit your applications to providers which are not the same as the cards you already have. You won't be able to balance transfer from one MBNA card to another, for example, or one Crapital One card to another, even if they're under different brand names.

2) Based on the foregoing, cancelling card #1 shouldn't make a lot of difference. Some lenders might look better on 2 cards than 3, but I've had no problems getting 5. The account will stay on your file for 6 years after you close it, so the only difference it makes is to the amount of available credit you have now. My gut feeling is I wouldn't cancel it... it might come in handy for a future balance transfer.

3) I can't tell you how each individual company scores your history, but 6 late payments in 3 years doesn't sound too bad from a card company's point of view; they got their money in the end, and some late payment charges too. This does not constitute a default; if you'd defaulted, you'd have been given a notice of default, referred to a debt collection agency and the card stopped on you.

You didn't mention which card providers you use, but if you happen to have a Barclaycard in the pack, then you may wish to know that they usually offer a lifetime balance transfer rate of 6.9% for existing customers (ring and ask, if applicable). It may be that an 0% deal is better for you if you can pay it off within a year, but this may be another option.