If this is an e-mail I would advise you to check your typos and make sure you have apostrophes in the right places. Some people don't care about such things but ask yourself if you would like to receive an e-mails which was clearly written in a hurry.

In general, this writing is ok. I don't see the point in correcting ALL mistakes as long as what you write is clear. However, I recommend you to read about the difference between "from" and "since". 

http://speakspeak.com/resources/english-grammar-rules/various-grammar-rules/since-for-from

Could you help with my very small writing, please? Thanks for your help.

Good day to you!
How are things? What's the weather like? Here, it is not chilly, and the temperatures are above zero and the snow has started melting. I hope you and your family are in good health and happy. [1]
I am doing okay [2]. Unfortunately, I couldnt couldn't write for a while. I was a bit depressed.
I mainly went to churches in central Moscow during holidays. I started working since from last Monday [3]. Again, I have to wake up bright and early and go to work.
I came come [4] home tired and ravenous. I usually have a bath and go to bed early.

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[1] I know this is just writing practice for you.  Even so, you should move this sentence to immediately after "Good day to you!"  You want to comment on your friend's happiness before you talk about the weather.  It is much more polite.  Here is what I mean:

"Good day to you! I hope you and your family are in good health and happy.

What's the weather like? Here, it is not chilly, the temperatures are above zero and the snow has started melting."

[2] The full word is "okay".  The abbreviation is "OK", but it must have capital letters.

[3] A native speaker is more likely to write the following:

"I went back to work last Monday."

[4] If you write "I came home tired", it refers to one day.  For example:

-- "Yesterday I came home tired."

 If you write "I come home tired", it refers to many days.  For example:

-- "Each night last week I have come home tired."

Since you are describing how you've been recently, the word 'come' is suitable.

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It's great to see you writing again, smelval.  I hope you keep it up.