1) The differences between the Taurian Concordat and the five Successor States is as different than any of the Successor States from each other. Basically, they maintain primarily Western European cultural heritage, with a focus towards France in some of its trappings. However, its government is not the same by any stretch and is a unique beast entirely. If anything, I'd view them as basically being the stubborn guy who lives on the fringes of society in a cabin, who has more libertarian views about everyone doing their own thing as long as they don't mess with him, and he is willing to shoot anyone who wishes to take what he thinks is his away from him.
2) Their leaders during this period of time were not exactly the one-dimensional paranoids that people joke about or think. Thomas Calderon grew up in a Taurian Concordat that was proudly independent of the Successor States, but extremely distrustful of them. Nothing in Taurian History, from first contact with the Federated Suns and Capellans, to the Succession Wars have proven that any of the Inner Sphere nations was worthy of their attention. When invited to join the Star League, they refused to give up their independence and kowtow to Terra. Over time, Thomas became more and more mentally unhinged as he watched all but one of his children die or be turned into invalids. Eventually, the Capellans and the Word of Blake were able to play the institutional hatred of the Federated Suns (who has caused more harm to the Concordat than any other nation, short of the now-dead Star League) into a blind rage as they pulled a Hilter-esque propaganda campaign.
To the concept of the average Mechwarrior being crazy, no more than any other nation. Some regiments (like the Pleiades Hussars) would fall into the 'crazy' side as they have almost deified their lost homeworlds in the Pleiades Cluster which had been ruled by the Federated Suns since they were conquered centuries before. They preached hatred to the occupiers. On the flipside, your average Taurian Lancer probably cares more about fighting pirates than any greater politics.
3) The Taurians view all other nations as outsiders, but the further they are from the Inner Sphere, and the less-aligned they are with the Federated Suns specifically, the warmer their relations are. They maintain longstanding ties to the Magistracy of Canopus (with one war tarnishing it) and the Outworlds Alliance. Unlike the Magistracy, they had cordial relations with the Marian Hegemony as well, and eventually warmed to the Word of Blake because they were offering apparently string-free gifts and infrastructure upgrades (and other things, too). They even eventually warmed to the Confederation, of which they have a long and checkered history.
Basically: They are not Taurians, so we don't entirely trust them, but those who are less likely to abuse us get a warmer welcome.
4) Your average Taurian probably wouldn't bat an eye to being a Mercenary, and wouldn't mind working with any of the Successor States. A few would have prejudices against one of the Confederation and (especially) the Suns, but no more than a Capellan would have in a mercenary group fighting for the Free Worlds League. It is all a matter of personal experience, and the Taurians value personal freedom above most, so as long as the Successor State employer didn't abuse them or get too 'into their business' they'd probably fight all the same. Mercenaries don't go into the mercenary trade because they are patriots, else they'd have joined their own militaries.