It doesn't matter whether you plan to extend your visa. The situation is that, even if you two get married, you are not entitled to apply for PR anyway. So the marriage status will have no effects on your BF's citizenship application.
By all means, however, your should keep your visa valid. If you are luck to sort out marriage and spouse visa before the expired date of your student visa, there is no reason why you shouldn't apply for a spouse visa straightly. Otherwise, you should extend your student visa instead.
Second question
part time or full time will have no effects on his citizenship application.