My Day of Christmas Day

"Christmas Day" is the way we say it in English

I spent my Day of Christmas quite well.enjoyed my Christmas Day

The correction above is also correct, but "I spent my day well" sounds unnatural to me. You might say "I spent my Christmas Day (with someone or doing something)" but to say it was good, it would be more natural to include it in the verb, or say something like "I had a wonderful Christmas Day".

My parents and I did many things in order to spent a great night, but we are onlyprepared a lot to have a great night. As we only have three people in my family, sowe normally we invited other people to our reuncelebrations.

I'm going to differ with the above correction a bit, my interpretation is a bit different. (It depends on whether you're talking about how you normally celebrate - which is what the other poster thought - or if you're talking about your preparations for this year, which is what I think)
Spent - you mean "spend" here (this is the infinitive, to spend, rather than the past tense). "To have" is more natural
It's difficult to keep the sentence going after this, so it's best to break it and start a new one. (The "As" I started with replaces your "so" - you invite other people because your family is small)
"Invited" - this is the present tense in English, not the past tense
A reunion is a specific gathering of people who have not seen each other for a long time (like distant relatives, or returning to school). "Celebration" is more appropriate for Christmas

We only invited only one person very close to our family, because in these tim this year. It was the best we wantecould tdo doin thate current circumstances.

"only" - reads better before not after "invited". The other user is correct that "this year", or something like it, is needed given what else you've written.
The other user's correction is a legitimate interpretation of what you've written. I've gone for something like "we couldn't get what we wanted due to the pandemic, but we made a compromise" ("current circumstances" = Covid-19; "the best we could do" = we couldn't have everything we wanted, but we did something)
Again I think this reads clearer as two sentences.

But, Iin spite of that, we spentall had a great night and dayday and night.

Spent is fine, had is more natural
The other user wrote "together", "all" is an alternative with similar meaning. You could also say "all had a great day and night together"
"Night and day" isn't incorrect, but it's unnatural - hence I've also said "day and night"

I Thank God for that.

Either my or the other user's correction is correct. It's perhaps a cultural difference, but I might say something like "I'm very grateful for that". It might be more natural.

My Day of Christmas Day

I spent my Day of Christmas Day quite well.

My parents and I dido many things in order to spent a great nightcelebrate occasions together, but we are the only three people in myour family, so normally we invited other people to our reunionevents.

"spend a great night" sounds like you're staying up drinking or going to a club, I think "celebrate occasions" is more suitable for a family event. If you're saying "normally", then it's habitual (not past tense). "reunions" would be appropriate if you only invited relatives (in the sense of "family reunion"), but you wouldn't call your relatives "other people".

WThis year, we invited only one person who is very close to our family, because in these times we wantedit is best to do thatso.

The time period has yet to be stated, which I presume is "This year...". The tone in "because in these times we wanted to do that" is mismatched... in the first part, it sounds like you're forced to invite few people (i.e. because of the coronavirus) but in the second part it sounds like you simply wanted a small event---I rephrased it in one possible way that avoids this clash.

But, Iin spite of that, we spent a great night and dayday and night together.

I'm not sure why, but "night and day" (even though it's correct) feels awkward here. Maybe saying "night and day" makes it sound like you stayed up all night with your relatives. It also needs a "together"; it feels wrong without it.

I Tthank God for that.