How to start/end an email to a hotel?

I need to email a hotel in Japan that I plan on staying at next year. This is the email I wish to send, however I don't know how to start it, or end it. こんにちは doesn't feel quite right.

すみません質問があります。2021年12月24日のチェックインと2021年12月31日のチェックアウトの空室状況は何ですか？ 部屋が利用可能な場合は、大人二人と子供二人のための価格は何ですか？ デポジットはありますか？ キャンセル料ポリシーとは何ですか

(English: Excuse me, I had some questions. What is the availability for the check-in on December 24th, 2021 and check out on December 31st, 2021? If rooms are available what is the price for two adults and two children? Is there a deposit? What is the cancellation policy? )

Last question, should I change the formalness of my writing? Perhaps make it more polite? I mostly ask because I don't want to come off rude!

Thank you!

Frankly I think it is clear what you want to ask but also clear that you are a foreigner (I am too). So I would just go with greetings that you know, because they will best integrate into the entire text. Eg a こんにちは at the beginning and a ありがとうございます　at the end should do.

I would also not up the politeness level. If you up it, you’d need to use through out for nearly every word a different expression. And you are using ますform so it is definitely not rude.

Plus I actually think that if you write in a way you can understand you have a little bit better chance to get a reply in slightly easier Japanese as well. It’s not guaranteed. Your counterpart might just use her/his professional Japanese. But maybe she/he is clever and understands that slightly less formal Japanese will be better.

The one thing you might want to change is instead of 何ですか　to いくらですか when you ask for a price. I am sure a Japanese can understand with 何 but it’s incorrect.

Enjoy your stay!

Your question to the hotel is for December 2021! One year later!
I think that reservations to the hotels begin normally 3 months before your stay, always with exceptions, naturally. Your Japanese is correct enough for Japanese hotel staffs to understand. However, for the time when you will really need to ask hotels in Japanese, I correct your Japanese like this:

失礼します。(来年の)予約についてお尋ねします。
2021年12月24日チェックイン、2021年12月31日チェックアウトの空室状況はいかがですか？ 部屋が予約可能な場合、一部屋に大人二人と子供二人の宿泊は可能でしょうか。それとも二人一部屋で、四人で二部屋ということになるでしょうか？それぞれの場合で価格はおいくらぐらいでしょうか？ 予約手付金は必要でしょうか？キャンセル・ポリシーはどうなっているでしょうか？

Even if you ask politely like this way, it is very possible that you will receive only an answer saying 「来年の予約については、今の段階ではお答えできません。適切な時期に当ホテルのホームページをご覧ください。宜しくお願い申し上げます。」

(>_<)