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.