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peakd.com seems to fix my #1 problem (wherein a new tab ignores my logged-in session on another tab). I am yet to know if my problems in #2 and #3 would be solved, although that means I have to move from hive.blog to peakd.com. I know that both are Hive (d)apps and are based on the Hive blockchain, but I learned a lot while I was using Hive.blog.

Thanks for your suggestion!

I noticed a problem with peakd.com while using Tor browser. Even though all the tabs share the same login session, I get logged out (on all tabs) every few minutes. I liked peakd.com's voting slider and more tips though.

just use hive keychain extension? should fix the problems

The Tor browser warns against installing any kind of browser add-on/extension, for fear that it would compromise my anonymity (such as leaking my IP address). This anonymity of mine allows me to say anything (except spam and hateful ones) that I would never say with a non-anonymous or semi-anonymous account.

Still, thank you for your suggestions.