I see that everyone is very confident about chipmixer, but how can you trust they really doesn't store the data?
You can't, in the same way you can't be completely sure that your Tor nodes/VPN providers/ISP are spying on your internet traffic or that this website is actually not an FBI honeypot. However, ChipMixer have mixed hundreds of thousands of bitcoin worth billions of dollars over many years, including some coins which agencies like the FBI were very interested in, and there has never been a single incident of data being shared, leaked, sold, etc.
Do you think that it increases the anonimity if I change BTC to Monero, send to another address and then back to BTC?
If you use two different non-KYC exchanges, you add in a few intermediate transactions, you don't swap the same amount, you do it over a period of days and not just immediately, and you do so over Tor, then yes, that would help.