Is the G535P good for competitive shooters?

Yes. Its surround processing is the main selling point, and it helps place footsteps and gunfire directionally. It is a reasonable pick for shooters if you want wireless without paying flagship prices.

How long does the battery last?

Logitech rates it at up to 33 hours per charge. Real-world use with chat and higher volume will land below that, so plan on charging roughly once a week for typical sessions.

Does it work with PlayStation and Xbox?

It connects through an RF USB receiver, so it works with anything that accepts a USB audio device, including PC and PlayStation. Xbox support depends on the console accepting USB headsets, so check before buying for that platform.

Is it over-ear or on-ear?

The cups sit on the ear rather than around it. That keeps the headset light, but people with larger ears may find it less comfortable than an over-ear design over several hours.

Can I use it for music and calls?

Yes, but it is tuned for games. The surround effect colors music and movies, and the boom microphone is meant for chat rather than professional calls.