No index. They directly correlate with Reddit, so if there is a Reddit subcategory, there is automatically an Imgur one. I'm not sure if they have an index, but you could check over there. 

The best way to look for new images is to check the new tab rather than the hot tab. They are placed randomly because their rank is determined by view counts and votes, which could place them anywhere on the gallery initially. 

Nothing wrong on this end. Pleasemake sure that your browser is fully updated, you have javascript turned on andyou may want to disable add-ons/extensions. You could also try it from anothercomputer or browser to see if you have the same problem.

We have plans for 2 and 3. I'll put a request in for one.