Welcome, Aleppane! Sorry to hear that money is tight–you’re not alone during these difficult times. It’s going to be tough without an instrument–have you considered renting an instrument? I did that years ago when screwing around with saxophone. Or, you could buy one of those Tromba/pTrumpet plastic horns, but renting one would probably be better–I have a Tromba flugel and C Trumpet…
Hard to answer your question regarding whether making a whistling sound is good or not. I don’t recall experiencing a whistling sound while playing the mouthpiece.
Playing the mouthpiece and leadpipe aren’t the same and are much more intense on our embouchure than playing the trumpet, if I recall correctly. My understanding is that “buzzing” our lips is THE most intense, followed by the mouthpiece, followed by the leadpipe, then the horn.
The best clue we get, in my opinion, as to whether or not we’re “doing it right” is with how it sounds and feels–if it sounds good and feels good, then it most likely is good; more specifically, when playing harmonic slurs–if we can play harmonic slurs such that we get a good sound, it feels relatively easy/efficient AND the sound is good, then we’re on the right track.
I suspect that’s why Greg focuses so much on harmonic slurs and did the “worldwide harmonic slur championship” a while back, etc.