Is it safe to add gas while downshifting?

It's called rev-matching.

Yes and if you do it really well you don't need the clutch.

Depends how you do it

Speed mismatch between engine and transmission is what wears the clutch. If you're applying throttle and holding it at like 5k for the shift and you end up at 3k once the clutch is out, that is going to wear it out more than just holding it at 3k for the shift.

That's fine. You are basically synchronizing the gears.

You can shift without a clutch. Give it gas to shift down, let off the gas to shift up.

This is the way. It avoids jerking and unnecessary wear when done correctly.

Its better for the car if done correctly. Rev matching.