There is no daily interest. Finance charges are applied to each bill that isn’t paid in full. Think of a credit card as a small loan, they let you carry a balance on which they charge interest and they require you to make a minimum payment. For example, let say you have a credit limit of $1000. During the month of February you spend $500, when your bill comes, if you do not pay the $500 in full, you’ll be required to do at least a minimum payment, usually around $10-20. You then will be charged interest on the rest of the balance. Of course if you pay in full, there is no balance and no finance charges. So, pay in full whenever you can.
Regarding your second question, again, think of your credit card as a small loan. If you are given a card with a $1000 limit, you can’t spend more than that. Your card will be declined if you try to use more (and your credit will suffer). At the same time, you can’t pay more than what the actual balance on your card is, that bank will not let you. In fact, sometimes you can’t even pay transactions that are still pending on your account. The bank will not let you do negative transactions as you say, because a credit card is not the same as a debit card. The only option you have in this case (with Capital One), is making an extra security deposit to raise your limit or if you have used your card responsibly wait until you get a limit increase by the bank (Capital One doesn’t give a lot of these though).
Also, when you first get your card, it can take more than a month until you get your first bill/statement. This is normal. As I mentioned before, just remember to always pay on time, even if it’s only the minimum, and don’t max out your card. Paying late will affect your credit, as well as using too much of your available credit.