If you're wondering about the placement of "me" in the second sentence, yes it is quite normal, as long as you follow with "a sandwich". Other examples include: tell them a story, write her an email, find us a place to stay... of course, no preposition when you put the indirect object (I think you call it Дательный?) between the verb and the direct object (Винительный). When you say, "could you make a sandwich for me, please?" (don't forget the please!), the focus is a little more on making the sandwich and a little less on who will receive it. But this is a really, really tiny difference. We may as well say both sentences are the same.

I understand that it sounds like you are asking to be made into a sandwich, but the possibility that you would ask that is so small, people will know what you really mean. There are many times that context and understanding save us from being misunderstood- hopefully. Let me think of another example.... how about: I am looking for a tall ladder to reach the ceiling. - Who will reach the ceiling? Will the ladder do it? That is what I said; but I hope we know it will be me that does it.

English is a combination of grammar and USAGE. If your teachers are native speakers of English, then usage is an area where they can help you. There are many expressions formed with the verb "make." "MAKE ME a ham sandwich, please!" or a sentence like that is a very common request. Also, there's another meaning of "make me," which makes the phrase familiar to us. "MAKE ME! I dare you!" is a common childhood taunt by a bully who doesn't want to do what is requested. If you try to force him to, let's say, move out of your way, he will beat you up. Well, if you want to say, "Could you make a sandwich for me?" then no one is going to MAKE YOU say it the other way. It's your choice, though I would add "please" to make your request more polite.

To any English person, there is no mistaking the meaning of 'make me a sandwich'; it's a standard phrase. There is no difference between the two alternatives. English frequently breaks its own rules of grammar and construction and is full of exceptions, idioms and phrases with obscure origins.

Both variants are correct. Using the modal verb "could" you make it a polite request for any context.