1. During towbarless pushback, the front gear of PMDG 77W is lifted up as normal, but meanwhile the Chaseplane camera is also lifted up as well.
If a camera is attached to a plane, is normal it would move with it,
2. When the front gear is lowered by the truck after pushback is completed. it hits the ground abruptly and even create smoke like a touch-down.
Normal, depending on flight model of the the plane used. Nothing we can do about it.
3. During towbarless pushback, the vertical speed indicator shows a negative reading.
Normal, because the plane is going in reverse, so it's likely having an effect on the VSI.
After the pushback, elevator trim is reset.
Nothing we do with GSX explicitly but, most likely, something the airplane code does on its own when it detects the airplane was raised/lowered during pushback.
Are these known issues?
None of these are even "issues", just normal consequences of the pushback and how the plane reacts to it. As explained many times on the forum, and on the GSX documentation, airplane develoeprs have all the documented means to detect if GSX is pushing so, if they feel some of their own internal simulations ( like ground handling, etc. ) could be affected, they can easily turn it off while GSX is pushing.
Of course, it's nothing we can do on our own, and it wouldn't be right if we tried to "hack" into the airplane code to turn off such system, because it would be very unreliable, it would likely stop to work with updates to the airplane code, and nobody is better suited than the airplane developers themselves to decide what to do if the airplane is being pushed, and decide how to react to it.