Is there a way to ask stockfish from the command line if a position is "quiet"? I am running a script like stockfish_fen.sh to return the analysis, but I would like to also know if stockfish considers this position to be of positional or tactical nature.
I don't think there is anything like that, and it'll never be implemented.
If you insist, you may want to look at how Stockfish does quiescence search. A "tactical" position would mean a dozen of long series of recursive calls. A "quiet" position would mean otherwise. However, this is a very dirty trick which might not work very well, you'd also need to do some programming.
There're other ideas, such as looking at the average branch factor, number of captures in the principal variation, the distribution of the scores... None of which is absolutely satisfactory.
No, there is not. This page describes commands: http://support.stockfishchess.org/kb/advanced-topics/uci-protocol
Also you can get information about Stockfish, with these commands, if you are on Linux:
stockfish --help man stockfish