Just a couple noob questions

[Xanithos]

Hello. I'm Zack and I'm a brand new Munchkin! I recently purchased the original, regular ol' Munchkin but have yet to find time to sit down and play. I've been reading up on it this whole week and played a few mock games by myself. I just have a couple questions, which I think I know the answers to, but just want some clarification, so here we go:

1.When anyone kicks down a door and the card is "MATE", that is just discarded as it has no effect, correct? A player can't bring in a Wandering Monster which then mates?

2. If I'm an Elf, and in my starting 8 cards, I get an item, for example "The Hammer of Kneecapping, which is only usuable by Dwarves. Can I still put that card "in play" but turn it sideways so it is just being carried, even if I don't have another 1-H item already equipped?

Thank you in advance. I'm sure I'll have more questions as I play!