There have been immense advances in technology for most aspects of people's lives, especially in the field of education. Now many students use the internet in order to find information, to do homework or research.

This is a good start. I just felt that the word "in" was used too many times so I choose to use "for" in one location so that the sentence flows better.

However, people are divided into two sides: half of them prefer studying online, but the other half do not agree with this opinion.

Since you've established that there are two sides, it flows better when you use the same structure for the rest of the sentence. Do you know what I mean? I wouldn't say "some of them" because it means you are becoming LESS specific, and this sudden change in certainty feels a little strange to the reader.

There are arguments in favor of both opinions. Studying online is convenient for scheduling. You will have a lot of free time and time for extra classes. This way of learning will save you money, because you won't have to buy a school uniform or textbooks, etc. However, online studying also has minuses. It leads to a decrease in peer communication, for example. And you have a great deal of responsibility. You will be responsible for your actions and marks.

You have established that there are two sides, and you are about to describe some of their arguments. So why not begin with a sentence which clarifies this, like "There are arguments in favor of both opinions". This warns readers and prepares them to hear two distinct opinions.

"Well it is convenient for the schedule" is too abrupt. It sounds like you are jumping to a conclusion before the reader has heard any of the arguments and opinions on the other side. It sounds like you're saying "Well it is convenient....do we really need to saying anything else?". The same for "besides, you will have a lot of free time". 

"So, online studying..." doesn't sound correct. This is the point where you give some arguments for the other side, so you want to make that absolutely clear. "HOWEVER" is a good word to use in this situation, it means that the reader has already heard one opinion and now they are going to hear another, probably contradictory, opinion.