Yes, by TM35.
no
Mewtwo doesn't learn Psybeam.
It learns Flamethrower at level 34.
It can learn Future Sight, Shadow Ball, Thunderbolt, Thunder, Flamethrower, Fire blast, Earthquake and many more moves.
I don't think there is a TM for it but you can get a Charizard, it will learn flamethrower, then breed that Pokemon with a Ditto, then that charmander should know flamethrower.
Palkia can learn flamethrower with a TM otherwise NO
Houndour will learn flamethrower at level 48
You only can learn flamethrower if you have a fire-type pokemon. Look for TM35.
All ground types can learn that like Golem, Nidoking, Nidoqueen. Other Pokemon that can learn it are: Aerodactyl, Mewtwo, Mew, Tauros, Machamp and many more.
Houndoom learns Flamethrower at lvl 48.
Vulpix learns Flamethrower at level 35.
I don't know all but slash flamethrower I think fire spin heat wave wing attack blast burn