Mega Alakazam it is.
You can have multiple Mega Stones, but remember that you cannot change items once the tournament starts, and you'll essentially be wasting an item slot as a result. I recommend not doing so, but I'm not going to ban it.
Castform is not going to count as a Fire, Ice, or Water type. If the Sun/Hail/Rain goes away, Castform reverts, I believe. That means it will no longer be following the rules.
As for Magnet Pull and Arena Trap, I'm not sure. I kinda forgot about those. I'm leaning towards banning those as well, since obviously Magnet Pull against your team would mean no switching whatsoever until you knock out the Pokémon. Arena Trap is a little bit more bearable, but... I dunno. Anyone else have thoughts on these? We never really addressed them in previous tournaments.
I like your badge - it looks awesome! And I'm also glad you picked Aegislash as your avatar, since he's awesome as well.
If we're going to ban Shadow Tag, I'd vote on banning the other trapping abilities as well. I think that's just Arena Trap and Magnet Pull. There's a couple of blocking moves as well, but those are weak and only count for the Pokémon currently active so I'm okay with those. I don't think banning two more abilities is terrible. (unless I missed something) Thanks for the rest of the answers.
Thanks! I like yours a lot as well. Simple but effective.