In Russian "first thing" and "first things first" are translated almost identically, so I can not understand when use one or another. For example you can say "We'll talk about it first thing in the morning". Could you say "We'll talk about it first things first in the morning" or not? If yes, then what is the difference between these two sentences? If no, could you plese give an example of two sentences where I can see the difference. Thanks in advance.
No, they are not the same in English.
"First thing" means... well, the first thing you do in a given situation. So you could say that you could do something "first thing in the morning" or you could say "I'll do it first thing when I get to work tomorrow."
"First things first" is a set phrase that only occurs at the beginning of a sentence, like "First things first, let's get this mess cleaned up." It roughly means "Let's get to work" or "This is the most important thing." It's pretty much always used to describe the present or the very near future, like a task to be done in the next five minutes, not "tomorrow."