please help me with this preposition

patience is the ability to be in the comfort with (I am not sure about this preposition. is it correctly? ) any discomfort.

The adjective "comfortable" works best here:

Patience is the ability to be comfortable with any discomfort.

Exercise, An email about computer use.

Dear Sam
I have just received your email, I’m happy to hear about you. It is a coincidence that you bought that CD yesterday, because I bought the same last week, although I bought it in a shop. I prefer to buy CDs in shops because I want to contribute with local business.
However, I use my computer for another things as to be in touch with my friends, so I am very active in the social networks, I have Facebook, Instagram and Snapchat accounts. Often I use my computer to study too, because is more comfortable and quick to research information.

I would like to see you soon!

Dear Sam
I have just received your email,.I’m happy to hear about from you. It is a coincidence that you bought that CD yesterday, because I bought the same one last week, although I bought it in a shop. I prefer to buy CDs in shops because I want to contribute with to local business.
However, I use my computer for another things, such as to be in touch with my friends, so I am very active in the social networks,. I have Facebook, Instagram and Snapchat accounts. Often I use my computer to study too, because is more comfortable and quick to research information. 

I would like to see you soon!

Nice. Just a few small problems with capitalization, mostly. Make sure you leave a space after a comma.

New Year's Day and Chinese new year  New Year

New Year's Day is January 1st, and it is the first day of the year on of the solar Gregorian calendar. Each year in  during this festival, my school holds a new yearNew Year's gala,so do this year. And my  My parents and i I watched the New Year's Eve Party on TV. Sometimes we go out for a trip with friends.

I think that it is all to celebrate New Year's Day. After all, it is just a common festival in China. However, Chinese new year New Year is a traditional festival which has a long history in China, it It is called 'Spring Festival' as well. It is in late January or early February for the most part, and it's the first day on the lunar calendar. We have a long holiday during this time.
As for me, I like Chinese new year New Year more. I can always get a great deal of money. Chinese people called it 'red pocket' or 'lucky money' and it is also a traditional custom, so the children are the happiest at this time of a year. Apart from this, my parents and I often do some shopping and cleaning, and we go to our relatives' s and friend's houses for a visit. People send gifts to each other. In On New Year's Eve, we often eat food like dumplings and spend the whole night together. The dinner is tasteful tasty and delicious, for it is not only a dinner but also a family meeting. We also watch The Spring Festival Evening Party and let of off fireworks.The sound of firecrackers don't doesn't disappear and lasts the whole night.
Anyway, Chinese new year New Year is the most important festival for not only my family but also every family in China. It is also the symbol of the arrival of a new year in China. Everyone thinks highly of it. No matter where the family members are, they will manage to go back home for family reunions.

So they are New Year's Day and Chinese new year. I estimate that you have further understood them now,right?

This afternoon

This afternoon,I did push-ups and plank.I love doing exercises!And I have abdominal muscles now.I hope that I can be stronger and have a healthy body! That's why I love doing exercises!\(^o^)/

This afternoon, I did push-ups and did a plank. I love doing exercises! And I have abdominal muscles now. I hope that I can be stronger and have a healthy body! That's why I love doing exercises!\(^o^)/

Nothing wrong here, but not all English speakers would know what a plank is in terms of exercise. I think it would be called "doing a plank" or "planking," which makes it a bit more clear. I added spaces between your sentences.

I completely forgot

I completely forgot that my sister came my apartment as I have been busy these days.
I was going to cook pork soup for her but I couldn't. There was no pork or some vegetables in the fridge.
I just buy rolled Sushi and fried some sweet potato and soy beans. but she said that was delicious.

I used past continuous tense, because it sounds like there was a plan for your sister to come to your apartment. This tense is for plans or activities that happen in the past and get interrupted. (Isn't English fun! : ) For example, "I was going to watch the movie, but I fell asleep." Simple past doesn't express the planned part. I added "past few" because it makes the time more clear. 

I completely forgot that my sister came was coming to my apartment as I have been busy these past few days.
I was going to cook pork soup for her but I couldn't. There was no pork or some vegetables in the fridge.
I just buy bought rolled Sushi and fried some sweet potato and soy beans., but she said that was delicious.

Is it correct ?

The rain had been watering us while we went down the street. I thought it could be better for us to wring clothes out in some hidden place, but we didn't find any. Suddenly, the rain was stopped and people started to appear from everywhere. All of them rushed by there deals didn't ever pay attention on us. All things around us were returning to casual life.

Lots of different ways to say this:

The rain had been watering It had been raining on us while we went down the street. I thought it could be better for us to wring our clothes out in some hidden place, but we didn't find any. Suddenly, the rain was stopped and people started to appear from everywhere. All of them rushed by preoccupied with their own business and there deals didn't ever pay any attention on to us. All things around us were returning to casual life.

You could also say "The rain had been pouring on us........" if you want to stress that there was a lot of rain. "Watering" is only used for plants. You could also say "normal life," but "casual life" is more unusual and sounds good.