Scarlet, You should not use "on" before "this afternoon" most of the time. If you wanted to say that the doctor's appointment was on one particular afternoon and not on another afternoon, then it would be proper to use "on". eg., Jim is going to see the doctor on THIS afternoon, not on THAT afternoon. If what you mean is that Jim is going to see the doctor today, then don't use "on".

Yes you can and its absolutely right also since you are using "on this afternoon" it means that you're talking about today's afternoon and not past days or future days. Hope this helps .)