Welcome to Gaia! ::

I'm not that confident in my Japanese but I'll try yum_puddi
My corrections will be below each sentence. The one's I've left alone are okay. I hope this helps! ^^ I'll be staying with a host-family in Japan too.

XXさんが、犬や魚を飼っていましたか、いいですね~ (You had a dog and a fish? How nice!)
]XXさんへ、犬と魚を飼っていますか？いいですね～

実は、のみXXは私のペットです。 (Actually, onlyXXis my pet.)
実は、XXだけが私のペッとです。((Actually, XX is my only pet.))

母と彼女の伴侶と一緒に住んでいます。 (I live together with my mum and her partner)

まとめてペットの世話をして、ですから大変じゃないです。(We take care of (our) pets together, therefore it's not that much work)
時々みんなは手伝いますから、ペットの世話をするのは大変じゃないです。((Because everyone usually helps [take care of pets], it's not that much work.)) I rephrased it differently to match your english translation but you don't have to use my translations ;D

今度、わたしが日本に来ているときは、家族が世話をします。 (During my stay, my family will take care of (our) pets.)
それだから、気になりません

私が日本に来ている時に、家族がペットの世話をします。だから心配しないです。((When I've come to Japan, my family will take care of the pets, so I'm not worried.)) 「気になりません」would mean you have no interest in taking care of your pets, or no interest in your pets at all.

日本の夏はとても熱いですね。(The weather in Japan is really hot, isn't it?)

ありそうな、日本の気候が疲れるなる、でも私は楽観的です。(Probably it will be wearisome to me, but I'm positive)
日本の気候は疲れるかもしれない、でも私は楽しみます。((The weather in Japan may probably be wearisome, but I look forward to it.)) Rather than saying "I'm positive" I used "Tanoshimi" because its more casual and neutral sounding than "rankantekidesu."

不安定な天気ので、ドイツで諸人が風邪気味だ。(The weather in germany is very unstable, wherefore a lot of people catch(ed) a cold.)
ドイツで天気が不安定なので、たくさんの人がよく風邪を引きます。((Because weather in Germany is very unstable, people often catch a cold.

こないだは３５℃でした、 ついで １６℃でした。(One day the temperature was 35°C and after that it was 16°C.)
例えば、こないだは３５℃でした。 ついで １６℃になりました。((For example, the other day was ３５℃, then it became １６℃.))
今、ぬくぬくとした天気です。(At the moment the temperature is cozy.)

XXチームから大学までの道は、少し気になりましょ。(I'm a little worried about the way from XXXteam(my host family likes to call themself a team x3) to university.)
XXチームの家から大学までの道は少し気になります。
手に負えるを願っています。(I hope I'll be able to handle that.)
大丈夫かな~((Will I be alright?)) in a suggestive tone. The translation you had was literally talking about your "hand" rather than "to handle a situation."

じゃあね~ (is that too informal?)
It's used between close friends, but I guess if you think it's okay then it should be fine. I don't think your host family would mind at all :333
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Thank you very much in advance emotion_smilies/icon_yatta.gif

(is this the right subforum for this post?)

Lol, okay then x3
Thanks for letting me brush up on my Japanese! emotion_bigheart

Haha, my pleasure! All the best to you! I can't wait till I get my letters in the next month or so~ >w<