I am talking about planets that revolve around one star in a binary pair (S-type orbit) and planets that revolve around both (P-type orbit).
I honestly think this question is more for the lines of google. I'm seeing it answered numerous times in numerous ways, allowing for creative thought and engineering to really become a "pick-and-choose" of what you would like to use out of the available information to construct your own working system. I've placed a link below as a good place to start, but the fact that you've already named the orbital types tells me you should likely know more than you're going to find from others on this site. https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems That being said, in a bit of imaginative sense, I wonder if planetary rotation and stellar orbit would be both greatly increased in speed due to gravity from two stars. Say if an Earth-like planet on around the same tilt access was subjected to a variable speed up, the seasons may be greatly increased in frequency, and the days may be extremely short by comparison, possibly only a few hours. The reason I ponder this is because binary stars are rotating at extreme rapidity, and likely centered on an extreme gravitational pull to create such a violent rotation. If I were you, I would download The Universe Sandbox off of Steam and play with the physics of a binary star system with planets in the habitability zone. I'd be interested to hear the results.
Well one way to make it work would be giant orbiting mirrors, to keep the poor little inhabitants from being cooked alive. Also it would artificially increase the length of 'nights' maybe? IDK, but heat would be a major obsticle to overcome, unless they just want to be living at the poles to avoid being outright baked in the light of two suns. Pretty much it offers less living space than a tidally locked planet to a single sun, cause then you have a livable strip of land around the planet with which you could survive on. I don't think if they have the capability to move the orbit of the planet would do them any favors, but if they could move one of the stars, then that would be the most ideal option. Or pick one of the stars, and do some extreme mining.
Well, that depends on the system. Some binary systems are very unstable, with planets just being ejected into outer space. Life on such a planet would obviously be impossible. There's a story about life on a planet in a binary system. I don't remember the name of the book, but it had 2 types of seasons. The small mother star around which the planet orbited was responsible for earth like seasons, the bigger one made seasons lasting thousands of years (kind like ice ages). This would probably happen if your planet is orbiting one of the stars and the star is orbiting the other one. Think of it as a habitable moon.
Astronomers have found a number of planets in orbits with binaries, but they're very unlikely to be habitable. A planet can not orbit both stars, that creates a three body system, which is inherently unstable. Not only is it unstable, but the players will make wild swings as the center of mass is constantly shifting. Your planet would likely be sent close to the star, then flung away from it, then be somewhere in the middle. No life could withstand such extremes, water would constantly be going between boiling and deep freezing. The only stable(ish) system is when the small planet is far away from a tightly orbiting binary, where the center of mass remains as pretty much a point. This means the planet is very far out, and will probably be frozen solid.
Where is it in relation to other celestial bodies? If it's really close or really far from a star, the orbit is going to be the least of people's worries. But it's not like that's completely removed from the orbit either. If, for example, the earth was rotating in a perfect circle around the sun, you would see a change in the equinox dates or something. But nothing major. However, depending on the orbit, you also have to consider the orbit of celestial bodies around it. If the moon was closer to the earth, then it would cause a shift in gravity which would cause a shift in the tide at the very least.
If the planet was in an S-type orbit, It would be a few miles closer to its main star than Earth is to the Sun.