Hehe, this is looking adorable. The first drawing really is very sweet.
Going down through your concerns,
This is what popped into my mind when you mentioned cassette player https://i.ebayimg.com/images/i/300893836407-0-1/s-l1000.jpg , has a bit of roundness to it like you mentioned and at least with a slightly older viewer it should bring back some memories.
The simple eyes from the first image are pretty delightful. No need to change them unless you really feel the need.
I did not pick up in the original image that it was a gun arm, just that it was another boxy part of the robot, and you do indeed need that element there just like you said it helps the comp.
Perspective- in your original image you had the perspective of something very close to the ground looking up, its cute, like another kid sitting on the floor watching, you can see it because you do not see the top of any of the boxes, only the side and bottoms. So I think that holding to that would be the right idea. In your painted image you are showing the top of the two boxes, and the angles of the box sides does not work with seeing that, nor the wheels or the ground. That is probably what you are picking up on there.
I will do a quick paint over and show you those corrections.
I love the wall paper and drawings idea for the background, we just put wall stickers up in my 4 year old boy's room to that effect. No furniture needed, the floor and the floor board will show plenty about where they are.
Its looking great, keep at it. Ill post the paint-over corrections in a few minutes.