I believe that when it comes to privacy and anonymity, you can't trust anyone at all. So what kind of information can a bitcoin mixer service get?
All they can get is your bitcoin address use for sending them coins with all past transactions, and IP address you used for connection on their website.
You can easily mitigate that and hide your real IP address with using Tor browser that is recommended anyway or with alternative paid vpn service.
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?
All this information is probably stored for some time on their servers, but good mixers will delete this data periodically.
My assumption is that some mixers could be operated by government organizations in same way like they run Tor nodes, so they will probably going to save all your activity.
You can use mixers multiple times making it very hard for anyone to read complete history for your transactions.
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?
I already answered this, and there is no need to ask the same question twice.
How can minimize the collection of personal information by mixers?
There is no ''personal'' information collected by mixers, it's just IP address and your wallet address, both of this can be used my multiple humans if they are shared.
You are again asking same question multiple times, and I said yo can use Tor browser or vpn, with good address management.