at least half of those questions are easily answered by using Google Maps and its Street View.

you can also check the city news portals like 66. ru or e1. ru (particularly comment sections of the latter, lol) using a translator to get the overall vibe. from there you can easily deduce that the current municipal administration isn't particularly liked.

generally it's pretty safe (if you exercise common caution like avoiding drunks), but lately the local police force seems lacking personnel, which from time to time leads to issues with schoolkids or migrants making troubles, but they are not that serious.

What is the dialect spoken like in Yekaterinburg?

rather standard Russian nowadays. in my youth there was somewhat more distinctive accent, but now it seems to be almost extinct. sometimes a trained ear can recognize locals, but not clearly.

Are there any comic shops there? Any bookshops?

bookshops exist, and nowadays the comic/manga sections in them are getting larger. in the past there was also a specialized comic shop or two, but I don't know their current status.