K^2

Your ideal landing should be the ideal takeoff in reverse. Of course, you can't mirror it perfectly, because the rocket gets lighter as the fuel gets used up, but this is the basic reason why the two delta-Vs are basically the same. P.S. You should budget extra for landings, though. It's very unlikely that you'll perform anywhere close to a perfect suicide burn, and if you brake a little early, you'll need extra fuel to fight gravity.

"Nope. Not going to space today."

You are thinking of optimizing delta-V for fuel. That's not the same thing as optimizing fuel use for LKO launch. I'm actually integrating over the entire trajectory using a numeric solver and all of the physics that goes into KSP. Engine mass affects how the ship performs in gravity and therefore contributes to the fuel-optimized result. Fact that I'm getting identical results for fuel consumption, height, and speed in game as I do in my computation kind of proves that I am looking after all the factors correctly. And the optimal operational range for first stage of a staged ship ends up being pretty specific regardless of design details.

Fuel and launch-pad mass are optimized by the same function. Slight variation for TWR of individual engines, but if you are using staging at all, that difference will be very much washed out by performance of lower stages. Definition of a payload is only relevant to a specific challenge, not to the optimization. And individual parts just determine how close you can get. So in the end, there is still just one good solution, dependent only on whether it's an SSTO or staged.

Fuel/Payload. Is there another objective function? EndOfTheEarth, if you are not burning prograde, you are wasting fuel. When you are burning downwards while still rising to apoapsis, you are wasting a LOT of fuel. Any optimal ascent to orbit will include a fast burn at the apoapsis. The only question is how much rotation you should do while you are raising the apoapsis. In vacuum, the answer is easy. You do the exact reverse of a suicide burn. With atmosphere, it's a much harder problem.

Because drag is proportional to mass, and because drag coefficients are pretty uniform, you can actually optimize the whole thing. The numbers I quote are within a few percent of optimal. And yes, I take into account changes in TWR due to fuel consumption. These are going to vary a little with the choice of engine, but for the first stage, the difference isn't huge. You still end up within a few percent of these values. Naturally, SSTO will be different. You are forced into sub-optimal regime by requirement that you reach orbital speed with single stage.

You should be past 15,000 km before vt begins to out-race your rocket. If you are seeing that happen at 10km, your rocket isn't quite powerful enough. Shoot for lift-off TWR of about 170%. You should reach vt about 40 seconds in, and your first stage should run out of fuel about 95 seconds in. This puts you about 17km up, 500m/s, and with vt racing ahead. Good place to fire the second stage.

No, you can't synchronize orbits in KSP. That requires perturbations or 3-body physics. Neither is simulated. On the other hand, orbits are perfectly stable, so if you have two orbits pass more than size of your satellites from each other, you'll never have a collision.

The main interest is in creating artificial gravity that points in consistent direction. Why? Because the higher acceleration you can achieve, the more efficient the launch can be. If you use magrail to launch from Moon, you can use shorter rail. You could shorten voyage distances. And don't get me started on what this can do for the military. Acceleration a pilot can withstand is one of the greatest limitations of modern jet fighters. It's part of the reason why un-manned anything is so much easier. There are two principle problems with using magnetic fields. Yes, you can attach magnetic particles to every single cell. This will allow you to counter effects on flesh. Not having your internal organs crush themselves is definitely nice. But typically, the first problem of over-G is blood pooling in "lower" parts of the body. You'd have to replace blood with some sort of ferrofluid, and these tend to be too viscous to act as plasma. Second problem is purely of mag-field permeability. Human body is filled with water. Water is a pretty strong diamagnetic. That means it actually provides some shielding from magnetic field. The effect is subtle at lower fields, but as the field strength gets higher, it becomes a serious problem. This is something you have to account for in MRI, and that's just 1-2 Tesla. So if you apply field strong enough to counter high acceleration, you'll actually be creating internal gradients that are causing problems. Of course, if all you want is create an artificial 1G, then none of it really matters. Blood will circulate just fine in micro-G, so applying a magnetic force just to cells that make up the tissues will be sufficient to replicate almost all effects of gravity. But as it's been pointed out, a centrifuge works just fine for that. I don't think convenience of being able to apply 1G linearly will outweigh inconveniences of working with high mag fields. Then again, with everything moving towards polymer construction and superconductors in space being relatively "cheap" due to vacuum being a damn good insulator, maybe it can end up being easier. Oh, by the way, you don't need nanobots for any of this. There are plenty of ways to bind magnetic particles to cell membranes. Not if you use superconducting magnets. These only require power for cooling, and that can be minimized in space.

Ionization plasma is going to be most intense when you pass the lower layers of ionosphere, maybe a bit lower. That's about 80-85km. That's not necessarily when you'll have the peak heating, however. Supersonic heating will depend on density, ambient temperature, velocity, and shape of the craft. So with other things being fixed, that's going to depend on re-entry angle and orbit you are returning from. Unfortunately, I don't know what is typical for that, but I imagine it's a bit lower.

Depends entirely on the orbits. Just because two orbits intersect, doesn't mean the two satellites can ever collide. If they are synchronized with some 3rd body, for example, you can guarantee that they pass through intersection point at different times. In LEO, it should be possible to synchronize orbits using the fact that Earth is a spheroid. In other orbits, you can use a moon. If the two bodies are massive enough to influence each other's orbits, really crazy things could happen. Consider orbits of Epimetheus and Janus for example. If you cannot guarantee synchronization, it's a question of how much the orbits are going to fluctuate. In LEO, the biggest enemy is drag. An orbit that decays is going to change both in period and in position. If the orbit is stable, on the other hand, you don't need much space. Just enough for the two objects to pass each other and maybe a bit for orbital perturbations. Finally, keep in mind that even if you have no control over the orbit, odds of collision are astronomically small. Have you seen maps of objects in LEO? And yet, there was ever only one collision between satellites.

Either of the two pictures are possible, and it has nothing to do with tidal interactions. If you give an object a bit of a nudge, it will just keep on spinning, its orientation constantly changing. If you give it just the right amount of push, it's rate of turn can match its orbit around the parent body, giving you the second picture. Of course, with real objects, you do have tidal interactions and axis tumbling, which will make the whole thing way, way more complicated.

Not every geometry conserves energy, but any physical setup will, once you take into account interaction between whatever masses you use to create wormholes, etc. GR absolutely does not allow for infinite energy generation. As far as what happens if you place two ends of a wormhole at different elevations, I'm pretty sure there is going to be a compensating gravitational field within the wormhole. You will lose the energy you gained falling from top portal to the bottom one somewhere. In contrast, if the portals are looked at as a teleportation mechanism, energy would have to be supplied by something. There is no other way around it. Of course, that would also result in quite a significant draft circulating between the two portals due to pressure differentials.