1. Well, yes and no. The Wyrmgates are orbiting their respective planets, so you can't just walk through one and be planetside, so there's that. I'm not sure yet though if I'm going to make them docking stations with individual portals to the different planetside settlements or if I'm just going to have them be what they're described as already. But to answer your question, as long as you can make it onto one of the shuttles or go through it with your armour then yes anyone can travel through them.
2. The majority of the planets are still uninhabitable for just about the same reasons as they are now. However that being said, there are colonies on these planets that allow for life to function normally. But without having a mech or being on one of the planetside trains you won't last more than a few seconds outside of the colonies.
3. If they can get on one of the shuttles or steal/earn a mech then they can definitely go through. Mechs are more or less waved through unless the mech they're piloting bears the insignia of a group on bad relations with another planet that is. If a teenager managed to get their hands on an Emergent armor for example, they would be subjected to several tests to check their allegiance. But if you just get on the shuttle then it's just a quick background check given by taking a piece of your dna and your name.
4. Yes. Almost without question. Since she is the right hand of Arthur she does have to give a quick background check to make sure you're not wanted of anything serious. But more often than not she does make exceptions.
It's no big deal haha. I think I explained those right. If you've got any more questions or want me to elaborate more on anything just ask :) You asking questions helps both of us.
