You know, I THINK the issue here is that you're mixing up force with energy with power. At least that's what i'm getting from the language in your post. But I'll do my best to answer your questions. Also, it seemed like you were trying to correct me about elliptical cranksets, but you don't seem to have done that in any way - unless I'm missing something.
But as for your questions:

Would you care to calculate how much force is required to lift your leg? Or do you imagine that lifting 10% of your body's mass requires no energy whatsoever?

Yeah, sure I could calculate that, I guess? Assume I mass 70kg, and one leg is ~15% for simplicity (closer to 16.7, but w/e) and the leg travels a mass-distance average of 0.2m (I'd do the real integral, but the assumptions I'd make would just add as much margin of error as this anyways) and at a cadence of 90 rpm. It looks like you're also talking about just lifting vertical, so we'll ignore the forward backward of traveling the crank if that's cool by you. Even acceleration gives us 1.2 m/(s^2). (70*0.15)kg*1.2m/(s^2) gives a net force of 12.6N. Add that to the static balance and I guess that makes it + (70*0.15)*9.81m/(s^2) which together make 115.6N.

Although, anything greater than the static ( > 103N) is enough force to move your leg but I don't think that's the answer you were looking for. But now I'm confused, because I'm not sure what you get from this. That leg has got to come up anyways otherwise you're going for a very short ride. So, am I missing something?

2) you're right that it's not designed to exert AS MUCH force as pushing down, for instance consider a flight of stairs that you have to climb up. but consider running where your forward step curls and you pull back on your leg until you push off from it. It's not as significant as the push, but it's definitely still there. So yeah, you're kinda right, you won't get as much from the pull as the push, but you certainly do get something.

3) Again, SORTA right. Yes, the more energy you put in just from a Cal perspective, the less efficient you're going to be (think driving 75 vs 35 in your car) but that doesn't have to do with the 'direction' of the force.

If you think differently, I'm not perfect, so let me know if I've made a mistake. I guess I'd rather learn something than be right, haha. But yeah, i hope something in here is helpful.