Can I exclude applications folder from my Time Machine back up?

Let me start with item 3:

Data is NOT stored inside applications, or even together with applications. It is separate, and it is saved in locations that are inside your home folder.

Hence, not backing up applications will not impede backing up your notes, mail, pictures, etc.

macOS is a multi-user operating system. Each user's data is separate from other user's data, and separate from applications, and the OS.

Regarding 1 and 2:

You can decide not to backup the Applications folder. That's fine.

If you are concerned with space, I suggest you just not backup any applications, regardless of them being the ones that come with the OS, or ones you installed yourself. You can always install those again, fresh from the developers' sites.

To exclude some locations from Time Machine, go to System Settings->General->Time Machine, click on Options... and then under "Exclude from Backups" click the + sign to add folders you want to exclude.

The System folder, which contains all of the built-in apps, is not backed up. Any apps you added are stored in an Applications folder in the Data Volume. I would imagine you would still need to exclude the main Applications folder to exclude that folder.