If someone gets physical access to my pc, mounts my ubuntu and changes my user password (e.g. in the shadow file).
Will he be able to log into my account and decrypt my (encrypted) /home partition?
Is the login password connected to the user password or are they fully separate?
I'm honestly not sure what you're asking, you seem to ask multiple questions.
What I get is, is that you're asking wether someone with physical access to your PC, can access your encrypted data? If a person has physical access, and your PC is running, they can at the very least access the decrypted data from memory.
If the PC is turned off, they will need your passphrase to access the data, this can of course be bruteforced etc. I don't see how changing your password in the shadow file and logging in would reveal the passphrase. According to Will changing password re-encrypt my home directory? your passphrase is encrypted with your password, so changing your password in the shadow file won't change the encryption of your passphrase.
No, nobody will be able to access your encrypted data without you passphrase.
This is the whole point of encrypting data.
