I banked with RBC and had a credit card through them. I asked them to automatically pay off my credit card balance (by automated transfer from my bank account) every month -- so that I never paid interest on the credit card, and never had to remember or forget to pay it. So it was similar to a debit card (though different in various other ways of course). Maybe TD would that for you too. I did it by going into a branch and asking someone to set it up (as you do when you open a new account).
And/or, to answer your question, I think you're allowed to transfer money into your credit card account at any time. You don't need to do it, though, before the "due date" on the monthly statement -- I think there's no interest charged before that due date (unless you use the credit card for a cash advance, in which case interest starts being due immediately, but you shouldn't/wouldn't ever use your credit card for cash advances, use your debit card instead).
Also, I don't have cheques, so could I use online banking (TD Easyweb) to pay my bills?
If you're asking about electricity bills and so on, I think you can set things up (with the provider, e.g. the electricity company) to let them to do direct debit from your account (e.g. by giving them your bank account details), or pay your bills via the web (the online banking web site), or perhaps give the provider your credit card details and let them charge that.
In general this is a question to ask the provider ("How can I pay you?") and the bank ("How can I pay them?"), it might vary from different providers and different banks.
I tend to prefer automated payments (and, I don't know, possibly some providers might expect and insist on that).