Can you use a pre-paid T-mobile phone using your T-mobile contract sim card?

It all depends if the phone is sim locked. There are never any restrictions on sim cards only on the phones you can use them in.

If you have a phone that you want to use was originally from Telstra either prepaid or from a previous contract it wont be a problem however if your phone was previously for example on a Optus contract your mobile MAY be sim locked.

It is not always the case that the phone is sim locked (sim locked means you can only put a sim card from the same company that originally supplied the phone) When purchasing a phone the best thing would be to check with your local Telstra or all phones dealer if the phone you are buying is sim locked to a particular phone company.