The military is usually depicted fairly kid-gloves, but then again you have organizations like Cadmus that are sanctioned by the government to kill or contain metahumans extra-judicially, so the goverment is definitely shown to be doing shady things in the shadows too.

Hmm, really it varies by writer as to how progressive he is politically. Generally his actions reflect his politics as they aren't outright stated. However, he's frequently championing social causes and doing things that help citizens directly but also stand in the way of regressive politicians and business leaders (Luthor being the most prominent of those). Unfortunately due to the majority of writers probably being liberal he doesn't often get quite to socialist Superman as he was in the very beginning. So yes, lib for sure in the tone of the politics that are there. Sadly with big corporations owning these characters the amount of political dialogue allowed is abysmal.

Although, the movie is suprisingly political and makes a comment (albeit in fictional, but easily recognized pastiches) about the Israel conflict and a Superman intervention into such a confrontation. It's refreshing to see. And from what I've heard it's triggering a lot of libs, conservatives and Zionists. Apparently Fox had some particularly vitriolic things to say about the movie's message (um, don't exterminate people indiscriminately I guess).