My boss ask me to install Time Machine in my computer to track my activity and take screenshots, but i'll not installing it because i'm remote and it's my own computer.

If it's your own computer, privacy would be broken. Good choice not to.

That fucking asshole of a boss should be doing his bloody job and follow your status reports on your progress,

If your boss doesn't trust you that you're working, either there's a reason or it's time to leave.

Also: as @Fast-Nop pointed out: are status reports and progress not.good enough!? Automated screenshots = watching over your shoulder = control freak = toxic environment. Leave.