How are thing  *This is plural, so you need to add a "s" to the end.* *things going at work and at home? What is the weather like? It is very cilly *chilly here *"Here" is correct but, since you also write "outside", it makes more sense to have either *here* or *outside*.* and gloomy outside. 

Things are not bad for me. The day went well and tomorrow and the day after tomorrow are week offs. *This sentence is very awkward, I would suggest rephrasing it "The day went well and now it is the weekend."* I like weekends*, you do not have to waky *wake up brigght  *bright and early and to * You will want to write either *and* or *to* as *and to* would not make sense in this sentence.* commute to work in an uncomfortable bus.
Today after work I went to the social service fund *A specific place or organization is capitalized* *Social Service Fund to deal with my issues. My mum *In British English you would use mum but in American English mom is used so this depends on what dialect you are learning.*  is entiteled *entitled to free bus ticket  *This is plural* *tickets. Unfortunately, they said that I must bring some other documents too. So I hope after work on Monday I will *can deal with it and with my divorce at the court. *Will means you absoulatley will do it, so you wouldn't use the phrase "I hope" when you know you are going to do something.* 
Since it was late*,I decided to postpone my visit to *the ancient church in the heart of Moscow on Sunday.
In a week, *my school are **Are* is plural while *school* is not, you will want to have either *schools* or *is*.* *is having a week break. During *a short school holiday *, you can take a day off at your expense ( so *So yoiu *you are niot *not paid for this working  *work *Working is a verb.* day). I would like to take a day off on Monday so next week I will have a long weekend.
I am going to meet with my ex *former  colleague tomorrow.
Have a wonderfull *wonderful weekend, rest welll  *well.

Can someone please correct my mistakes? Thank you.

How are things going at work and at home? What is the weather like? It is very chilly here and gloomy outside.
Things are not bad for me. Today went well and the weekend starts tomorrow. I like the weekends because you do not have to wake up bright and early and commute to work in an uncomfortable bus.

Today, after work, I went to the social service fund to deal with my issues. My mom (unless British) is entitled to a free bus ticket. Unfortunately, they said that I must bring in some other documents. I hope after work on Monday I will be able to deal with it and also be able to deal with my divorce at the court.

I decided to postpone my visit to the ancient church in the heart of Moscow on Sunday. In a week schools are having a week long break. During which you can take a day off at your own expense (you are not paid for the day you take off). I would like to take the day off next Monday so I will have a long weekend.

I am going to visit my alma mater tomorrow.

Have a wonderful weekend and rest well.