Im wondering is there any ways to make this possible:
I have a nstextfield(or nstextview). And I also have one button, clicking on that should activate Bold mode for selected text, or the text that would written further.
First idea I had - is to use attributes for characters that would be written further, but this idea is not so good, as I would need to save that string in file later. I can save attributed string, but this gives me not proper format, what I would like to see is kind of or smth like that.
If I understand correctly your "First idea" is correct. Within your program you use NSAttributedString to add bold etc. your text. When you wish to save the text you can convert to HTML, or a number of other formats, and reading these formats and converting back to NSAttributed is also supported. A good place to start is Formatted Documents and Attributed Strings.