よろしくおねがいします。ケイシアです。私の文章を正しますください。

I'm still learning the kanji to apply to my existing vocabulary, so my writing is a mix of basic kanji and hiragana. I'm interested in grammatical accuracy and contextual nuance. (辞書を引いています… "正しい言葉を使う"と思います?)


今日の文章:
大変です! 今日は家のエアコンをしにました。今はすずしいシャワーがいいです。今週末はベースメントにねます。

Today's text:
I have a problem! Today, the air conditioner in my house died. A cool shower would be good right now. This weekend I will sleep in the basement.


Notes:

For mentioning the problem, I wasn't sure whether "大変です" or "困っています" would be more accurate. I know "大変" has connotations of "rough," "tough," "hard," so I went with that, since being without AC in the summer is pretty rough. "困り" seems more like "troubled," but I don't have as much context for it.

"家の" — I think I've seen this used as both "our" and "of the house," so I figured it was suitable. "My family's air conditioner" and "the air conditioning in my house" are interchangeable for what I mean. I know that "our" is "私たちの". Should I have used that instead?

"エアコン" — I've heard this used in anime. Is it the most common word used for "air conditioning" in Japan, or is there a native Japanese word that I should use instead?

Died: quit working. I'm not sure what the right word is in Japanese, so I used "しにました". At this point, I only know that and "なくなりました", which I think means something more along the lines of "left" or "lost" or "passed away." Is there a word specifically for objects or appliances that don't have a literal life?

I don't know the word for "basement," so I used katakana. Is there a Japanese word for a finished room underneath the house? Not a cellar or a foundation, but a livable room.

ありがとうございます。 Thank you for your time!