I'm not an expert in the field but from what I know, SHA1 is a one way function. When an encrypted password is cracked, YES, the hackers know that specific password. They brute forced it by guessing the password, running it through SHA1, and comparing the output to the hash. If they are the same, then they guessed the right password.

They do not know any other passwords and if "salt" was used, they would have to brute force each password. I think salt wasn't used in this case so once they crack someone's password, they know every other user who used the same password. So if you and I used the same password, and they brute forced yours already, they will know that I have the same password.

"Cracking" in this sense is brute forcing. SHA1 is fast, and people use bad passwords. The combination means that you can run through lots and lots of bad passwords very quickly. I checked my linked in password I have stored in 1password, and it is 20+ chars with special characters and numbers. That won't be "cracked" in any meaningful sense, so I don't even worry about it.

You are correct that there's currently no way to go from a hash to a value that hashes to it in SHA1 (AFAIK, IANYNSA [I am not your NSA]).