Today starts a new month, a month I hope it's will be funny and happy.

It's been 2two months since I started in langcorrect, althought I had good and bad moments, I can say my learning was success.

Today I want to give thanks to God and everyall the people that I helped me in this process.

I hope continue to improveing and learning more things about this language, so I hope my family and your family (people that are reading this letter) bare well.

A nNew mMonth

Always capitalize the first word and every first letter of each subsequent word.

Today startsmarks the beginning of a new month, a month that I hope it's will be funny and happy.

I'm not exactly sure if you meant "funny" as "fun" or if if that was truly your intention, so I'll just leave it as is.

It's been 2 months since I've started in lLangcCorrect, a. Althought I had good and bad momentsome good moments and some bad ones, I can say that my learning was an overall success.

Today, I want to give thanks to God and every peoplerson that Ihas helped me during this language-learning process.

I hope to continue to improve and learning more things about this language, and I also I hope my family and your family (people that reading this letter) be, as well as you and your family, are doing well.

Today startsis the beginning of a new month, a month that I hope it's will be funnyfull of fun/laughter and happyiness.

It sounds more natural to say “today is the beginning of a new month”. You could also say “today marks the beginning of a new month”.

You could start a new sentence instead of having the comma there.

I’m not sure if you need the “that” because of grammar rules, but personally I prefer it with “that”.

It sounds a bit more natural to say “full of fun/laughter and happiness”.

You can choose between “fun” and “laughter”, or you could also keep both so it becomes “full of fun, laughter and happiness”.

It's been 2 months since I started in lusing LangcCorrect, a. Althought I had good and bad moments, I can safely say my learning whas been a success.

It sounds better to say “using LangCorrect”. The better preposition than “in” though would be “on”, because “in” kind of implies that you’ve been living inside of the website.

LangCorrect is the name of the website so it should be capitalised.

I think it’s better to start a new sentence, but if you really wanted to keep it all as one it would be better to add in an “and” before “although”.

Adding in “safely” is optional.

“Was” wasn’t technically incorrect, but it felt like you were reflecting on the past two months and had decided that you were going to stop using the website entirely.
“Has been” is better for if you’re planning on continuing to use this website.

“Success” is a noun, so you either need an article (“a” in this case) before it, or you would need to change it to an adjective. If you changed it to an adjective, it would be “I can safely say my learning has been successful”. But in this case, I prefer how “a success” sounds over “successful”.

Today I want to give thanks to God and every peoplone that I helped me in this process.

After “every”, you would have a singular noun. So technically you could say “every person”, but “everyone” is more natural and concise.

In this case, having I in “I helped me” doesn’t make sense, since it would kind of override the idea of others having helped you.
However, in a different case where you actually want to use “I”, then you would say “I help myself” or some other variation depending on the tense.

I hope to continue to improve and learning more things about this language, so I. I also hope my family and your family (the people that are reading this letter) are/will be well.

I think that in most cases, “hope” would be followed either by “that” or “to…” (e.g. to continue).

Since you said “to improve”, you would say “learn”. You could also say “to learn”, but the meanings are slightly nuanced. I think “to learn” kind of separates the two ideas a bit more than “learn”, which keeps them connected.
Based on this though, you could also keep it as “learning” and instead change “to improve” to “improving”.

“So” implies that there’s a connection between the two parts of your sentence, but I can’t really see a clear connection between the two so I think that what I suggested should be good.

Not having “the” in front of “people” feels kind of colloquial and rushed (like I can see someone writing it like that if they were planning something out and wanted to write down the idea before they forgot it). It also could be viewed as really confrontational, which could be interpreted as being mean.

Before an “-ing” verb like “reading”, I think that most, if not all of the time, you would need another verb like “am”, “is”, “are”, etc.

You can choose between “are” and “will be” depending on your intended meaning. “Are” is for hoping that they are well right now, and “will be” would be more for the future. But I think that if you want to directly include the future it might be a better idea to say “are and will continue to be well”. However at the same time I think most people would assume that you’re helping that they will be well in the future as well if you hope that they are well in the present, so “are” is probably the better option in my opinion.

A nNew mMonth

Today is the starts of a new month, a month. I hope it's will be funnll of joy and happyiness.

It's been 2two months since I started in lwriting on LangcCorrect, a. Althought I had good and bad momentmy ups and downs, I can say my learning journey was a success.

Today, I want to give thanks to God and every people that Ione who has helped me in this process.

I hope to continue to improve and learning more things about this language, so. Furthermore, I hope my family and your family (people that reading this letter) bare well.