1) agreed. there's solid evidence that Mars sends junk to us - not sure about the other way around.
2) does that matter, since they're in orbit, thus zero/microgravity? You still need energy to leave an orbit, whether up or down, I don't see how it makes a difference. There's no friction to speak of to make "down" a direction that things are predisposed to move in. Over ridiculous time scales sure, but ridiculous time scales are nothing like human time scales, so we still have many orders of magnitude difference if we fling stuff at Mars intentionally.
orbit. gravity is canceled out by orbital velocity, as far as distance-from-sun is concerned. it costs Mars nothing to stay in orbit, and to go down to a -100m/s orbit or up to a +100m/s orbit costs the same amount of energy: (mass of mars) * (100m/s velocity change)
if Mars and the Earth were not orbiting, I would completely agree. drop something from Mars and it'll land on Earth, and the reverse is not true. but they're not - drop something on Mars and it's just in Mars' orbit.
Delta-v requirements for transfers in space are generally symmetrical. It takes the same amount of delta-v to go from Earth's orbit to Mars's orbit, for example, regardless of direction.
The one thing that changes this equation is aerobraking (or, when dealing with stuff whose structural integrity isn't important, lithobraking). Because drag works in one direction, that means that you can take advantage of it when arriving but not departing. For that reason, for example, it takes more delta-v to reach a transfer orbit to Mars from Earth than it takes to reach Earth from a transfer orbit to Mars. Technically that's not true, but when arriving at Earth, a great deal of delta-v can be provided by the atmosphere or the ground.
It's true tat it's been a long time since I played with this stuff, I work out for a circular orbit
Total energy of an orbit is -G mp mS /(2 r)
mp = mass of planet
mS = mass of sun
r = distance of planet from sun
Even though this is a circular orbit, the basic result should be the same: the greater the distance from the sun the more energy the planet has, per unit mass.
I think I understand your basic point, however, which is that whether we speed it up or slow it down we have to do something to the mass, and how much we do depends only on difference of the orbit radii.
But note that adding 100 m/s or subtracting 100 m/s gives two different differences in r.
About #2, it may be the other way round, anything escaping Earth is easily pulled in towards Mars' orbit by the Sun's gravitational pull. The other way round, it requires more energy to escape.
1 - Less gravity on Mars -> smaller escape velocity
2 - Mars is in a higher energy level (gravity wise w.r.t the Sun), so Mars to Earth is "falling down", but you need energy to go from Earth to Mars