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
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.
Houndour will learn flamethrower at level 48
You only can learn flamethrower if you have a fire-type pokemon. Look for TM35.
I don't know all but slash flamethrower I think fire spin heat wave wing attack blast burn
Mewtwo is good for beating the elite four (2nd turn), since it can learn moves like Flamethrower, Thunderbolt, Ghost Ball, Phsycic. All these moves are good since they're all special attacks and Mewtwo is one of the best Pokemon in sp.atk. These moves are also super effective versus almost everyone in the elite four and this enables you to beat the elite four fairly easy the 2nd time.
Houndoom learns Flamethrower at lvl 48.