めったに〜ない

あまり cuts how much of an act happens (あまり食たべない). めったに counts how often it happens at all (めったに食たべない).

時々ときどき admits the times happen, and treats that as normal (時々ときどき失敗しっぱいする). めったに〜ない says it almost never happens at all (めったに失敗しっぱいしない).

めったに counts occasions, so it needs an event that could repeat (めったに来こない). ほとんど measures quantity or proportion, and works on one-off states, which めったに cannot.

めったに counts occasions and says they almost never come round (めったに飲のまない). なかなか instead says a wanted occasion keeps not arriving, and carries real impatience.

よく says the act is the normal thing (よく行いく). めったに〜ない puts it near zero, and always needs ない (×めったに行いく is wrong).

ろくに also needs ない, and says the act was done badly (ろくに読よまないで返事へんじした). めったに says the act almost never happens (めったに行いかない).