5
At the time of writing, Ash has owned 15 of the 18 types through by either catching or trading
The only types Ash does not own are Psychic, Ghost, and Fairy.
Source
2
Meowth can't evolve because he can't battle.
As stated on Meowth's Bulbapedia article:
Meowth normally does not battle unless there are extreme circumstances; his explanation is that his ability to talk and walk upright came at the expense of battling ability.
A good example of this is Pokémon: The First Movie, where Meowth and his clone are two of the ...
1
In different view to F1Krazy's answer, I would like to point out that evolution has shown to work differently in the anime it does in the games.
There is no apparent leveling system in the anime, so it doesn't make sense for Meowth to have "acquired enough experience" for him to evolve.
Trade-revolutions are also shown being handled different, as with ...
1
for the first question
In the first season ep75 "Bad To The Bone!" a guy named Soto has lost all of his badges to Team Rocket saying "All our struggles and sacrifices were for nothing", meaning he can't just go and claim his badges were stolen, but in the 5th season ep45 "Why Wynaut!" after Ash's badges were stolen Clair the gym leader tells him "If you ...
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