"My second question is how many openings is need to be somehow mastered to get some progress at the beginning of the game?"
None. At your level, at my level, openings don't determine the outcome of our games. Find the openings you like to play, and gain some understanding of "why" the pieces, and pawns go where they go. You will get a lot farther ahead by doing that, as opposed to blindly memorizing moves, with no understanding of the "why" behind the moves.
How can you know if you are a good chess player according to Chess.com ratings? My rating is 1400-1500. My subjective opinion is that I'm a solid chess player, but not a good chess player. My second question is how many openings is need to be somehow mastered to get some progress at the beginning of the game? I'm limited only to one opening with white and two with black pieces.