1,

That sounds perfectly normal.

2,

I don't fix mine down but I would suggest a hot glue gun if you decide to - definitely no tape inside the enclosure. I don't fix mine as it allows me to move it around and check different areas like inside the hides etc.

3,

It probably won't affect it much but I would definitely check the first time I had it on.

4,

I've never seen one of those so I can't help I'm afraid.

Maybe use something non-flamable to rest the edges of the lamp shade section above the mesh of the top? You would need to double check it didn't heat any part of it to dangerous temps though to avoid the snake getting burnt.