I haven't used tails but I know about tor:
- I've never logged in on any website by using Tor (browser) because I was afraid someone would be able to hack my accounts and gather my passwords. Is it safe to log in to my e-mail (no, not my personal one!)? What about BitcoinTalk or a decentralized exchange like Bisq? Does logging in through Tails make it more possible to have my passwords stolen if I log in to them?
You can log into other sites freely using Tor, if you want to keep your anonymity up there may be ways to isolate different parts of your desktop although I imagine tor tabs can't interact with each other anyway (much like firefox ones can't unless you add a script).
When connecting to tor, your information is encrypted at every hop and there are layers of encryption, it's like an onion.
If you've hidden a note inside a gold onion, have 3 runners and the king you're sending your note to.
1st runner, peels back their layer with a key
2nd runner peels back their layer with a key
3rd runner peels back their layer with a key
Then king then has the final key to gain access to the note.
1 knows who you are and that you sent an encrypted note to 2 and so on but they don't know what the note is and they don't know all the hops it took, they just knew the last hop and yours.
If runner 1 and 3 were in kahoots, they'd know every hop but as long as you have HTTPS enabled (and if you click the padlock when you go to the site you can check it's authenticated - I'd trust QuoVadis or Comodo CA to be distributing authentic licenses).
- How do I SAFELY download things that I can also open (say an image or a video) through Tails while also online? I heard it's not a good idea at all to open files downloaded through Tor and knowing the fact that Tails enforces any connection to run through it, I guess it's not the best idea to download stuff and open them later..
The thing with downalods is that even an image can contain a tracker or something to hijack your machine. If you trust the source you downloaded it from and accessed it via an encrypted source then you're fine to open it. A bit of a difference with tor is that if there's a warning triangle next to the padlock with a line through it this means some media is NOT encrypted by the source server and I therefore wouldn't trust it.
(I've spent too much of my day discussing european royals)