I can't believe it--I wrote a whole long reply to this, and it disappeared from my computer! I have to get going on a trip, but I'll see if I can give some ideas quickly here. And, of course, others have played this music and will be able to make great contributions. In the meantime: starting at the end with the big trill, you have to just experiment to find your favorite fingers for doing a long-ish and loud trill. Actually, at tempo, it doesn't last that long. But if you haven't trilled a lot, it could feel long! For me, 1 & 3 is a strong combination because of the extra space of the unused finger between. That space feels like a little fulcrum to me, and I rock back and forth around it. I don't really trill in the fingers; I mean, the sensations for 0me are in the back (top?) of my hand and in the forearm, that I'm rotating or wiggling, making the hand turn (but my hand stays aligned with the wrist/arm). You'll want to notice, also, that the violin is really slammin' here, with big lush bowing and double-stops, so your trill is more like a bed of sound for the soloist--so don't get too worked up about it, just enjoy it. For the same reason, it doesn't need to be so fast that you set the keys on fire. It's more important to be physically comfortable than to work up speed on purpose. If you're comfortable, the speed will happen all by itself, so the speed is not the goal, the comfort is. The little turn at the end doesn't have to be as fast as the trill, either. If you're sweating the timing of it, then plan a rhythm for that last beat. So, you could trill "openly" for three beats, then do a triplet (c,b,c) on beat 4. Or if you accidentally play the turn early, just hang tight and wait for the next downbeat. It will just sound like you're being dramatic, it won't be wrong. DO NOT lose sleep over this! For the jump down, I suggest looking at the keyboard, not at your hands. Stare at middle C like your life depended on it, and your hand will arrive there just fine. Don't watch the RH make the jump. You already know where your hand is. What you need to know is where the C is! Also, if you can think of the jump as more of a slide or shift sideways, rather than arc-ing up through the air, you'll cut out the vertical distance and not have to travel as far, if you see what I mean.
Jumping to the beginning, Ms. 19 trills, you only have time to do a little triplet on the first half of beats 3 & 4, so don't bother with anything more elaborate. I would start both triplets on my index finger, but of course that's up to you. The slurs call for a lift, which gives you permission/time to move your hand in between.
Ms. 38-45, can you specify exactly what feels awkward to you here? Is it jumping from chord to chord, or making the chords sound even, or...? Not sure what to answer yet.
Ms. 100 etc: I see what you mean that it's a little odd to start the triplets staccato, then change later. My guess is that the pianist in your recording was responding to the (partially) staccato triplets in the violin part. The answering parts (quarters, half notes etc) are the same idea in both
parts, but the triplets are different material, different ideas... so I'm not sure why they treated them the same way. Does it sound good? I mean, it wouldn't bother me to hear it like that, it might be a little harder to do. Then when he changes to legato, I see that that's where the violin part changes material-- double stops etc, so maybe he was trying to reflect the new moment or something. Anyway, I think you could defend a range anywhere from pretty smooth to pretty dry, I wouldn't go to an extreme either way.
To answer another question, I'm a teacher and a performer. I like to teach mostly beginners, because it's such a special time, but I like to solve problems at all levels... or at least try!
I hope any of this was helpful. I'm going to be gone for a while. If I can't check back in, don't think I forgot about you! Others will certainly be helpful as well. There are some fantastic pianists on the forum. Good luck!