So far I have found and verified that Kraken.com works with yubikey, I will do some more research today if there are more useful sites that use yubikey 2FA.
And of course, you can configure 2nd slot (the long press) as static password, so anywhere where you need a password, you can use it. It's a random set of either 16 or 32 alphanumeric characters, so it's always more secure than any password you can create and remember yourself. It is of course always the same fixed string (until you reconfigure it again), so it's advisable to add some prefix which you easily remember for each place where you use this fixed password, so that you won't have the same password everywhere where you use it.