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I believe the answer to your first question is the film Robots where the main character looks much like you described him
update: I went to youtube, and stumbled apon a playlist called "cringe" one of the videos had a character that looked like the one I talked about...
it was rolie polie olie
Funny thing is that i used to watch that, I was at least close with the robot part, But on the bright side you found the answer to your first question so I wish you luck on the second.
he was that silver character with small black eyes and a red polygon on the front of him. One more thing; he was my favorite character, so I don't know how I could just forget him like that XD
1: this isn't a show, but a character, I just remembered a white robot with a head similar to that of a Lego figure, what I mean is; there is a black stud on top of it. I think he also had small eyes with blue hair or something like that. I don't remember his name or anything.
2: I remember a theme from a show on treehouse that starts at night, then a few seconds later it becomes day, the show might have been stop motion, and I think it was from the uk.
Edited by cake64