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Hello!
How are you doing? What's the weather like?
I hope you are doing great.
The weather is good here but from time to time it is a bit windy.
These days I am volunteering Recently I have been volunteering at a in Bulgarian church.
Recently + present perfect continuous needed. Indicates you started in recent past and are continuing the action.
One of the workers got ill and while she is recovering I am helping [out] there.
I am gradually overcoming my depression step by step and soon I hope it will fade away in the near future. Perhaps ‘clear up’/’improve’ for ‘fade away’.
My daughter is staying at my sister's. She likes to sleep there.
In three weeks I am going to have take a summer holiday. My colleagues and are counting down [the] days till our much deserved time off the anticipated deserved holiday. These year we [will be going] go to the Black Sea again this year. Remember. Adverbial phrases of time usually sound better at the end of a sentence.
My daughter is looking forward to see[ing] the sea again.
Unfortunately, I have no time to spend on my English or and in reading.
That's all my boring news
Waiting for [some] good news from you

Well written! Just think where best to put your time adverbs. Also, did you know that thyroid problems are a physiological cause of depression, so maybe if you get the treatment you talked about earlier it may help. Best wishes. :-)

Could you help me with my post? Many thanks in advance

Hello!
How are you doing? What's the weather like?
I hope you are doing great.
The weather is good here but from time to time it is a bit windy.
These day I am volunteering in Bulgarian church. One of the worker got ill and while she is recovering I am helping there.
I am overcoming my depression step by step and soon I hope it will fade away.
My daughter is staying at my sister's. She likes to sleep there.
In three weeks I am going to have summer holiday. My colleagues and are counting down days till the anticipated deserved holiday. These year we will go to the Black Sea again.
My daughter is looking forward to see the sea again.
Unfortunately, I have no time on my English and in reading.
That's all my boring news
Waiting for good news from you

Could you help me with my post? Many thanks in advance

Hello!
How are you doing? What's the weather like?
I hope you are doing great.
The weather is good here, but from time to time it is a bit windy.
These days I am volunteering in a Bulgarian church. One of the workers got ill, and while she is recovering, I am helping there. (it may sound less formal to say "and I am helping there while she recovers")
I am overcoming my depression step by step, and soon I hope it will fade away.
My daughter is staying at my sister's. She likes to sleep there.
In three weeks, I am going to have a/my summer holiday. My colleagues and I are counting down the days till the anticipated and deserved holiday. Thise year, we will go to the Black Sea again.
My daughter is looking forward to seeing the sea again.
Unfortunately, I have no time to spend on my English and in reading. (here you can also say "I have no time for" or I have no time to work on" or "I have no time to practice", but any of the choices is okay) 
That's all my boring news.
I'm waiting for good news from you.

One other note is that if you use British English, taking a holiday (or going on holiday) is generally the same as taking a vacation (or going on vacation) in American English.

Purple = I added something

Blue = I changed something

Green = notes when you have other options to say the same thing differently. I usually explain whether it's "to sound more natural" or just a list of options.

Red and strikethrough = this should be removed

Very good! Your holiday sounds fun.