Hi.
I'm sorry, there's a mistake.
A room is open. = 部屋が空いている。　It's not 開いて.
“Open” is “開く” but we don’t say “部屋が開く”.
We can say “ドアが開く”　but it’s not what you want to say.
I think you means it’s available, so we should say “部屋は空いている”.
Translating too directly makes many mistakes.
We pronounce both of them “あいて”(開いて、空いて), I typed a wrong kanji.
Sorry!:ywave:

P.S =追伸
Is you don't understand something about my translation, ask me.

I've never used any online translators.

Just a small correction, most likely a typo ;)

Why didn't I think of that!

While the translation given is perfect...

I still think it would mean a LOT more to the family if you actually went through the effort of writing it yourself - or even just sending it in English.
Everyone seems to think it`s wonderful and impressive for them to send a letter in Japanese to their friends / host families, etc in Japan... But really it`s not. Either they think that you`ve written it yourself and are disappointed when they find out you didn`t - or know from the start you had it translated and are a bit disappointed anyway.

This is a really good point; you probably don't want to give them a false impression of your linguistic capabilities.