Re Trump and Putin, Trump wants an end to the unwinnable war, and is hoping that Putin can be cajoled into an agreement because it is costing him too much (in money, troops, & political cache).
It is worth a try, but as you know, Putin is a bastard, and he may well choose to find excuses to keep it going.
Where Trump needs to be careful for is letting Putin play it along too long if he isn't serious.
There was also the Zelensky problem because he was also in no way willing to end hostilities without getting back wall of Uk's land first - but that just isn't going to happen. He is also getting a lot of personal gain, and he has taken the opportunity set up a dictatorship (well beyond just suspending elections indefinitely as we have already discussed - Z eliminated the other 9 rival political parties and he has banned churches as well, and of course, he cannot account for all of the money that we have been sending him).
He is dependent on our money, and Trump brought him into line (for the first time).
So some progress has been made, but now we are at a point where we can see what Putin will actually do.