In forthe last few years, studying online has becaome a very popular typmode of studying in all educational institutions.

(1) I'd suggest the addition of a comma.
(2) mode: a way or manner in which something occurs or is experienced, expressed, or done.
(3) "Educational institution" is the proper phrase.
(4) "Educational instutition" should be plural, since the set of all education institutions contains more than one institution.

But what isare the advantages of that.is?

(1) It should be "are" and not "is", since "advantages" is plural.
(2) In the subsequent sentences, you use "this" instead of "that", so for consistency's sake, you can consider using "this" here.

The fFirst, it is very comfortable,: you can study with a cup of coffee or tea, or just step back for a few seconds with out questions ofa teacher.

I'm not certain what is mean by "step back for a few seconds without questions of teacher", so I took my best guess at it. Maybe you can provide me with the native text.

Also, when you stay inat home, you never forget anything.

Alternatively: "when you stay in your home". However, "when you stay at home" is more concise and probably more natural.

And the most plus of that typbiggest positive of this mode of studying it is mainly that it is cheaper.

(1) positive: a desirable or constructive quality or attribute. Alternatively: "the biggest advantage".
(2) "This" might sound more natural than "that".

But what isare the disadvatages of this?

MThe main thing is (the) lack of communication with people.

And it is true, definitely true, for all online studying, that you can't see noanybody.

(1) "Definitely" should be placed before "true". The way you wrote it has a different implication, though it is subtle. I shall not explain it for now, as it might be a little hard to grasp.
(2) "you can't see nobody" is actually correct, but it's slang. When writing in standard English, we'd use "anybody".

But after that,the problems do not end (there).

Very often during, when studying i, I had a lot issues with my laptop or internet connection, and mainostly it was not my guifault.

(1) You can consider commas here.
(2) "During" is used with nouns, so alternatively, you could write: "Very often, during study".
(3) "I" is always capitalised.
(4) "Mostly" is more natural than "mainly" in this context.
(5) fault: responsibility for an accident or misfortune.

As aIn conclusion, studying online has got a lot of advantages, but the absensce of communication does for me omakes offline studying for me absolutely better.