1. The second star doesn't orbit the first. Because any two stars in the main sequence will be relatively close in mass, both stars will orbit around a common centre of gravity, an imaginary point called a barycentre. Technically, all pairs or bodies, including the Earth and the Sun, are in mutual orbit around the barycentre for that system, but as the Sun is so much more massive than the Earth, this barycentre is still inside the Sun. It's not at the Sun's exact centre, but nor is it far away.
You have two main options here, which informs the answer. Do you want a Close Binary pair, where the stars are close, between 0.15 and 6 AU say, and if you want Earthlike habitable planets then the lower the better within this band. If you're not familiar with the term, AU means Astronomical Unit and is the average distance from the Earth to the Sun, roughly 93,000,000 miles or 150,000,000 km. Then all the planets orbit the stars' common barycentre, basically. This gives you a Tatooine-type sky. The other option is a Distant Binary pair, with a separation of say 120 AU upwards, and 200 - 300 is better for Earthlike worlds. Planets will then orbit each star separately, so star A has a set of planets and star B has its own set.
Based on the rest of the question I assume a Close Binary pair, so the answer is 0.15 to 6 AU, any value between 0.15 and 0.4 should suffice. This puts the barycentre at an average distance (technically semimajor axis distance) of 0.07 AU from star A and 0.13 AU from star B.
2. The answer to this depends on the stars' luminosities and the orbital eccentricities about the barycentre. I've used formulae from a Youtuber called Artifexian who's done a good series of videos on this, restating equations into relative-to-our-Sun type units. The rule of thumb for luminosity is mass cubed, giving us 0.51 of the Sun's for star A and 0.09 for star B. This means the habitable zone, where water will be liquid on a planet very similar to Earth, is closer to the stars than for our Sun.
The guide for eccentricites, how far skewed from a perfect circle the orbits are, is 0.4 to 0.7. 0 is a pefect circle. I picked 0.4 and 0.41 for A and B. The closest they ever come to each other is therefore 0.12 AU, and the furthest apart is 0.28 AU. The pair of stars create a nominal zone, within which their gravity will destabilise a planet's orbit and either tear it apart or fling it out of the system. The inner and outer edges of this zone are 1/3 x Minimum sep. and 3 x Maximum sep. respectively. So no planets could orbit between 0.04 and 0.84 AU. This makes it less likely that you could have a habitable Earth as the third body within this system, but let's plough on.
The base line for the habitable zone is square root of the two luminosities added together. 0.51 + 0.09 is 0.6, √0.6 ≈ 0.7746 AU. The inner and outer edges, using a conservative take on a habitable zone, are 0.95 and 1.37 times the base, so 0.736 to 1.061 AU wide. That will fit Earth at our 1 AU nicely, although we'll be further out, hence colder. We can't move Earth to the baseline itself as that's still inside the riptide zone, which extends out to 0.84 AU. Say we moved it to 0.91, that would still be closer, cooler than we are here but still in the zone, and with a 'year' of 0.776 years or roughly 284 days.
But please remember I've used someone else's simplifications aimed at building systems similar to ours, not necessairly at modelling K-type stars, I'm not an astrophysicist. My mate who is will be dealing with small children right now, it's too early for her to check my working! Sorry for any oversights. If you read up on Ks and find the luminosity to be too low especially then that throws all the habitable zone numbers out as they're all driven exclusively by that.
Questions 3 and 4 I can't answer, sorry. I think you'd be best hunting for one of the star system modelling programs out there as the fancier ones can not only give you better figures than I can, but can also model what things would look like from arbitrary points on the planet's surface. I can't recommend any right now, I've only got a tablet to hand for now so can't install anything decent, it doesn't have the power or the input tools (keyboard, mouse). But the answer will vary depending on where the stars are in their orbit around the barycentre relative to each other and the planet you're on.