In Generation II (Jotho) Bayleef learns these following moves by leveling up:
no
No.
claydoll learn hyper beam. self destruct, earthquake, and sandstorm; it can also learn phsychic
Um when it lvls up to a certain point
Gyrados can learn Ice Fang when leveled up. If you chose TOTODILE as your starter Pokemon, it will also be able to learn Ice Fang.
Bayleef Does Not Learn Sleep Powder in HeartGold/SoulSilver
depends on what level he is
Pokemon cannot learn Yawn in Pokemon Silver.
bug attacks
Vileplume, Paras, Parasect, Chikorita, Bayleef, Meganium, Roselia and Shaymin all learn Aromatherapy via level up in Diamond/Pearl.
It DOESN'T learn overheat. You can teach it but it doesn't learn it naturally.
if you have the machine click on it and if there is the word ABLE on it, it can learn it
Bellsprout.
fire Pokemon
no
See the related link.
No, it is not able to learn cut.