You are now Water and Fighting!

I thought you used the last letter of the above pokemon to determine the first letter of your new pokemon's name.
For example Para-Dox used Crobat, that ends with t
So our next mon might be Trubbish.

Trubbish has become the Fighting/Ground type, according to your post.
Ends with H so we have . . .

The way you play is to take the last letter of the previous Pokémon's name (Mawile) and pick a new Pokémon that starts with that letter, and then give them a new typing based on how you think they should have been made. Mucus used Trubbish, so now I'll use:

Heatran! And he'll become a Fire/Rock-type because I'm certain he's practically a living volcano.

Trubbish being Fighting/Ground makes perfect sense, because garbage is placed into landfills, which essentially fight with the ground. >.> :P

NoctowL becomes Psychic/Flying, because with Talonflame's precedent, there's no longer a reason for a starter bird to have to be Normal/Flying.

Lugia becomes Psychic/Water, because he is The Guardian of the Sea, not the sky!

Alomomola is now a Water/Fairy type. It so needs something else to it, and it seems to fit in with the new fairy types being pink and having little wing-fins.

Aipom became Normal/Fairy because it's too cute not to be a Fairy type!

Meowth is now a Dark-type because it lears A LOT of Dark-type moves via level-up. And it looks evil to me.

Haunter and his family are now Ghost\Psychic
why are they part Poison type anyway?

Roggenrola is now Rock/Steel because, according to Bulbapedia, its body makes metallic sounds when knocked.

Azurill is now Water type because seriously, why is it a Normal type? Do I have to explain?

Lickitung is now Normal/Dragon, because it's always reminded me of a komodo dragon.

Galvantula is now Electric/Grass because he lives in the grass and Bug has never done him well as a type.

Altaria is now mono Flying because as much as I love Altaria, it doesn't really look like a Dragon type what with the clouds and all.

Alakazam is now Dark/Psychic because I'm certain he's the only one powerful enough to manage the conflicting disciplines.

Mawile is now Dark/Fairy, because it's the Deceiver pokemon.

Eelektross is now Electric/Water because eels typically live in water (though with that typing, Eelektross wouldn't have no weaknesses anymore).

Scyther shall now be Bug/Fighting, ninja skill

Relicanth will now be Water/Ghost as it's practically a living fossil of a fish!

Hydreigon, Dragon/Fire, Badass

Making Nosepass rock/steel! Just sees like the type that would considering what its nose can do.