Would you anticipate classifying the other civs we meet as friend or foe, and then sticking with that classification throughout the game? Don't think of this as a yes/no question, please elaborate.
I think that making a judgement at the beginning of the game and then blindly sticking it to it for the rest of the game is a recipe for disaster. While we may initially intend to befriend one civ and make an enemy out of the other, there are many external circumstances that may come up (explained in the next answer), and there is nothing stopping our opinions of other Civs from changing from one turn to the next.
What factors should be used when deciding how to handle the other civs?
The most obvious factor is the Aggressive personality trait. Most aggressive leaders will usually turn on you later on in the game, so it's not worth investing too much time in developing a "life-long" friendship. However, if we do manage to befriend an aggressive civ, they may turn out to be a useful war ally...
Another factor is their location. If a civ is bordering you, I find it's good to make a good friend out of them (despite the "Our close borders spark tensions"), because if you ever end up in a war with someone else, your friend civ can act as a "buffer", and if you can get your friend to declare war on your enemy, then that opens up another front against your enemy, but further away from your borders.
Thirdly, religion is a key factor. It's so much easier to make a friend if they share your religion, than if they are a different one (especially if they are spiritual). If I manage to find a civ with no religion, I convert him to my state religion as fast as possible to secure another friend.
Last but not least is the civ's score (in relation to other civs). Allying with strong nations will get you farther than allying with weak ones. Civs with higher scores will often have better techs and/or more gold - and if you are friendly with these civs you will get better trades, or maybe even stuff for free! (I love it when that happens)
There are many factors that go into deciding how we should treat, or respond to actions by, another civ: it is not black and white. But the most important thing in the early game is to try to be as nice as we can - there's no use risking a war this early when we have no one to back us up. It's better to let the game follow its course a while longer so we can be more educated when we pick our friends and enemies.
What interactions do you see between your department and others?
At first, the most interaction the Secretary of State has is with the Minister of Technology - as it is a direct result of his decisions for when I can begin trading gold and techs. After Alphabet and Currency have been researched, I will work with the Minister of Technology to see which techs he would be willing to trade away, and which ones he'd like in return. I will work with the Secretary of War (and President for Naval units) because my political moves should fall in line with his military plans, and vice versa. Also, if he needs to upgrade our military, I can change my stance on trade so we can get more gold to fund the upgrades. Finally, I will work with the Censor because sometimes my job involves changing civics or religion as requested (or demanded) by other civs. Since my hands are tied on these decisions, I would work with him so we can know ahead of time, according to the votes by the Citizens Assembly, what course of action we should take.
Are you willing and able to assume duties of other Triumvirate members, if needed?
I am always willing to go above and beyond,
whether or not it is asked of me. That's one of the major reasons why I'm a student at such a great university.