Requesting a new circuit will get you exactly that -- a new circuit. It does not mean that Tor won't pick the same exit again, and it will not clean any cookies. It is trivial then of course for a site to recognize you again.
What you want and what was already suggested is "New Identity". Unfortunately, Tor Browser currently has to restart to get you a ...
To address some of your concerns:
"As I understand it, when logging in to a website, my username and password can be stolen when I send them through Tor."
This is more generally true of the internet, the proper solution is the application of end-to-end cryptography. For example, that the sites should use HTTPS, if HTTPS is properly deployed a passive ...
Welcome to Tor community! So - step by step to your questions:
No information, including login and password can be stolen if it's transferred via HTTPS and the certificate genuinity is verified. Use Perspectives project and/or Convergence to check it all up locally and in decentralised manner - it will save your day not just inside Tor, btw.
Tor is a very ...
The Tor Project put out a basic obfs4 Transport Evaluation. The pertinent quote is:
The (obfs4) design improves on the vulnerability to censorship based
on active attackers identifying suspect flows and attempting to
confirm which protocol is running via active attacks
The page goes on to say that it would be very difficult and expensive to try to ...
Sometimes websites will block Tor users because they can't tell the difference between the average Tor user and some malicious or automated traffic.
Source: My favorite website is blocking access over Tor!
Wait for an hour and try again. You might also want to try Telegram Desktop.
Google makes me solve a CAPTCHA or tells me I have spyware ...
It depends on a website and on blocking mechanism used. If it's a by-ip basis block - then all the exit nodes can be disallowed to login and you have no luck. In this case a VPN will help you. If it's not this case - try switching an Exit and you will be lucky one day
Logging into accounts associated with your identity is inherently not anonymous, but Tor will still hide your physical location (i.e. what internet provider / Wifi hotspot you are using at the time) from the sites.
However, you should not mix logins into sites associated with your identity with anonymous browsing in the same Tor Browser session.
The current Tor Browser doesn't really support this. The best workaround would probably be to somehow start multiple instances of Tor and connect through them. You could run multiple Tor instances with their own data directories, specifying different ports and then open up multiple browsers to proxy through the individual ports.