Well done! Articles are very difficult for native speakers of Russian

If you have a moment, how would you state 2 and 6 in Russian?

Thanks so much!

V

articles

1) There is the forest near our village
2) The sun has disappeared behind a THE clouds
3) Do you study a chemistry?NO ARTICLE NEEDED HERE
4) He knows the girl standing near tree.
5) Is the Don a deep river? PERFECT
6) Pass me the biscuits, please PERFECT
7) The letter written by you yesterday is still on the table. YES. 
8) When do you have a breackfast?   BREAKFAST. This is an exception ot he usual rule of article before noun--- similar with where do you have lunch, have dinner, have snack, or Where do you eat breakfast, etc   or Where do you DRINK... 
9) I'm going to spend my summer holidays on the Baltic Sea. ON THE BLACK SEA (in a boat) or AT THE BLACK SEA.
10) The village where my grandparents live is situated on the bank of Baikal Lake.GREAT

articles

1) There is a forest near our village.
2) The sun has disappeared behind some clouds.
3) Do you study a chemistry?
4) He knows the girl standing near the tree.
5) Is the Don a deep river? Отлично!
6) Pass me the biscuits, please.
7) The letter written by you yesterday is still on the table. Молодец
8) When do you have a breakfast?
9) I'm going to spend my summer holidays on the Baltic Sea.
10) The village where my grandparents live is situated on the bank of Lake Baikal.

These are good.  Any English speaker would understand you.  I have a Ukrainian friend who speaks and writes better English than most Americans, and he still sometimes struggles with articles.

We usually put "Lake" before the name of the lake.  "I go fishing in Lake Lanier." "I want to sail across Lake Erie."

"The" refers to a specific item among many items.  "I want to buy the red shirt."  There are other shirts, but I want THAT red one.

"A", "an", and "some" are not specific.  "I want to buy a red shirt."  I don't have a particular shirt in mind, so ANY red shirt will do.

Also, we and the British use articles differently, but we still understand each other.

I hope that helps.