I'm using Arena 3.5.1 with Stockfish_8_x64 engine. In engine output window it proposes best moves with different continuation variants and values. Can I add few arbitrary moves there myself and ask engine to calculate it values?
No. By definition an output window is for output from the program. You can only use input methods to input data. To do this just make the move you want on the board and see the computer analysis for that move in the output window. To do this for several different alternative moves create separate variations, one for each of your alternatives.