Does TimeMachine backup second user?

Time Machine runs at the system level and backs up all users, as dialabrain indicated.

It does not matter whether you are logged in as one or the other user, if any administrative user has set up Time Machine to run, from the System Preferences Time Machine Preference Pane, it runs automatically every hour ad everything (except things explicitly excluded) is backed up.

The first question is easy. Time Machine backs up everything on the drive unless excluded.

The second question is a bit harder. I don't use multiple users so I have to make an assumption. I would enable Time Machine in both users.

When you inspect the files in the Time Machine backup, as you were doing, those files retain the same permissions/restrictions as the user account files. So you won't be able to see into folders/files that are owned by another user, when logged in as a different user. If you log in as that other user, then you should be able to see and inspect that user's files in the Time Machine backup. You can restore any of user A's files when logged in as user A, and you can restore any of user B's files when logged in as user B. But user A cannot see into user B's folders, either on the main drive nor on the backup drive, and vice versa.

If you need to restore the entire disk, or migrate all users to a new machine, then all files can be copied/restored/migrated when those actions are taken because those actions are taken at the system level, not at the individual user level. But again, when logged in as a specific user, the user account permissions apply to looking at individual files/folders.

If you use "clone" backup software, such as CCC or SuperDuper, you will notice the same handling of user permissions on the backup drive.

Time Machine does not run at the user level, it runs at the system level. Each user has access to backed up files according to their permissions. The best way to restore files for a given user is to log in as that user and enter Time Machine to retrieve those files. I would leave things the way Apple has them as defaults, changing permissions around can cause problems if you make an unintentional error. Connecting two Time Machine disks is good practice, the backups will alternate between them and it makes no difference which user was logged in when those Time Machine backups were set up or activated. So what you are suggesting will work but you are adding unnecessary complexity and modifying permissions is not recommended.