1. Well I mean it was obvious in the movie that it's something that warns him of danger around him.
2. Probably not. Considering it's used in aircrafts. Although Peter might have done something to it so it dissolves, y'know, so people don't realise it's from Oscorp or something.
3. I posted a reply to this already, lol.
4. Probably just how a real spider sticks to surfaces. Because it's in a human and not a spider, it's probably strong enough to work through less than an inch of rubber. But it's probably weaker in his feet if he's wearing shoes.
5. Well, the hints are in the movie. He's looking at Luge suits online. The shoes are... well, from shoes. The lenses are from sunglasses.
He might have ordered 2 suits like this or something:
Then he could have cut them up into the base red and blue suit before adding the fine details with the silk screen press.
Peter also has a 3D printer in his room, so he could have knocked out the frames for his lenses using that.
And yes it is stretching out the origin for longer than needed, we don't really need to know any of these in extreme detail. It would have been cool to linger on some of these (like the suit) for longer than they did though.