I'll try to help:

Pick up the trash can and put it on the table
Подбери мусорный ящик и ставь его на стол(?)

No offense, but I don't like your shirt
Не обижайся - но мне не нравится твоя рубашка(?)

I am putting my clothes in my suitcase
Я кладу свою одежду в чемодан

For "get out of here", I'd stick with just Иди отсюда - уходи doesn't sound right, and I think it's too final. You might even say "брысь"...but that's for cats, I think - rude for people. If you really wanted somebody to go away (and possibly not come back), you could just say "уйди".

Мой плеер заряжается - I don't know if you can say "I'm charging the player" - because you're not, the electricity is...but I could be way over-thinking that...

The computer froze - компьютер отказал - but that could mean other things besides just "froze", I think

EDIT: You're too fast for me, Kwatts !