1) Mixer knows BTC address from which you send and knows the address to which you receive. Is information about the connection of the sending address with the receiving address saved? If this info is stored on their server, having access to this info, you can unravel the entire chain of transactions?
They can indeed do such connections if they want to, and even sell to chain analysis companies. In theory.
In reality I'd expect that they erase as much information as they can (and as early as they can) to avoid headaches from authorities (and also boast about this to their potential customers).
2) If the mixing service provider is a website, then it can get various information, such as an IP address and location? What can the mixer learn about its customers in this way?
It has been proven that clearnet websites of the mixers are pretty much under constant attacks. Putting them into the protection of cloudflare and such is something I've seen done by some of the mixer businesses, but it's wrong, exactly because then (also) cloudflare can get (some of) this information.
So the solution is simple: use the mixers that offer TOR addresses. This way you protect yourself from this (valid!) situation.
3) What information about users can generally be stored on bitcoin mixing service servers? If attackers / hackers get access to them, then this can be used to the detriment of users, right?
I am not that "advanced" in this, but I expect that the best mixers keep only the minimum information to ensure customers' money is not lost because of various mistakes.
But source transactions (and obviously source addresses) and also the resulted funded addresses should be there, together with some unique ID or session information the user may receive before starting the process.
Of course, as you stated, IPs can also be stored, but only on clearnet.
4) How can minimize the collection of personal information by mixers?
Access them only under TOR, be careful to not make mistakes (which can reveal more info about you when you ask about them), withdraw the mixed coins to your wallet (obviously to different addresses), never mix from or to centralized service (exchange)... I don't know of anything else. Don't mix overly big amounts in one step.
5) What other weaknesses and vulnerabilities are there in the scheme "your address 1 - mixer - your address 2"?
Make sure the mixer you use is known, has a good reputation and it's highly professional. Because if they're not, you may face "vulnerabilities" (intentional or not) you may not like (and the service provider may or may not be aware of that).