1. There's no need to remove her to count the eggs. If you just want to know how many there are, just visually check as best as you can by looking underneath the tub along with the ones you can see on top. She probably wont be too happy with you trying to candle them, but you can try if you'd like. Right now it's best to not disturb her too much.
2. Egg looks fine to me
3. Tub looks fine
4. Anything you can do to add humidity will be beneficial. Adding moss, some light misting of the bedding, etc.
5. As far as warning signs, not very much you can do about that while she is incubating them.
6. You could transfer the eggs, yes. They will all be stuck together so as long as you don't place them in odd angles they should do fine.
7. If by partially uncoiled, you mean how she looks in the picture, that is fine. It looks like a good sized clutch so she wont be able to wrap them fully. But it's in the ambient temperature is what matters more.