Is there a limit to how many things we can have in our: 1: Wardrobe? 2: Vault? 3: Inventory?

1. one of each wearable
2. as far as I know, no limit
3. no limit, but you'll only see 100 (different) items at a time in it, and you can't buy items from the shops if there are 100 in your inventory

I'm pretty sure that you can buy items from the official Subeta shops with 100+ items, it is just player shops and scratchcards that you can't.

There are around 10,400 wearable items on the site; you can have one of each in there. If you try to put doubles in, it will tell you 'you already have that item in your wardrobe!'.