1) What is the best Pokémon move?
There isn't really one single "best" move, but some of the good ones in competitive play are like Knock Off, Scald (and Steam Eruption, since that's basically Scald on crack), Stealth Rock, Volt Switch, U-Turn, etc.
2) What is the best Pokémon type?
These days (in OU) I'd say that the "best" types would be Steel, Fairy, Electric, Ground, and, to a lesser extent, Water and Dragon.
3) Who is the best Pokémon?
I mean, they had to create a whole new meta above Ubers just for Mega Rayquaza so ¯\_(ツ)_/¯
4) Who is the toughest Gym Leader?
It'll vary somewhat depending on your team composition (fighting Gardenia with a mono-Rock team is not fun) and battle style, but in general Clair and Lenora have been a little rough for me.
5) What was your favorite Pokémon game?
Right now I wouldn't say one specific game but rather Gen V as a whole.
6) What was your first starter?
Was Pikachu, since my first Pokemon game was Yellow, back in the day.