Doid you konow I was to going to come back to my home next on Monday?

"Did you know...?" is a set phrase in English. We use the past simple tense.

We say "next Monday" or "next week on Monday".

But my mother wantend to cancel my reservation.

I am writeing to you and imagineing to prepare to prayer and have a breakfast .

It is difficult to know when you did these things. Was it in the past? Is it in the present?
If you are doing something right now (in the present moment), you should use "I am writing to you".

As for me, yesterday was a busy day to make. I had to do a lot of things.

Remember to use a space ( ) after a comma (,).

I'm so happy to applychieve and to respect my goals.

Be careful, are you happy now? Or were you happy yesterday?
If it was yesterday (in the past), use "I *was* so happy to achieve..."

I would like to continue day after day, step by step, without stopping.

I feel strongly Ithat I will able to fight until tohe end.

My plans for today, I were to wroite three texts in English and in Spanish.

Or you could say: "Today, I wrote three texts in English and in Spanish."

It's the first step to improve my skill writing skill.

In tThis afternoon, I will listen to a story in English and I will looking up the words in the dictionnary.

After "will", we use the 'infinitive' verb. E.g. "go", "listen", "eat", "look". There is no -ING at the end.

Yes, I will make a promise byto myself.

Be careful with tense. Did you make a promise in the past? -> "Yes, I have made a promise..."

Also, if you say "by myself", it means "I made a promise without anyone's help".
But, "to myself" means "I made a promise for me and I will keep that promise." <- I think you mean this one.