Seeing as there's no one else on at the moment, I'll take this one.
Different factions have different laws about immirgration, and even emirgration, so it'd difficult to pin point exactly what question you have, but I'll just try to answer your examples, and then fill you in.
Why can't a Freespacer join the Star Army of Yamadai?
Yamataian society can be rather xenophobic, for Freespacers in particular the SAOY launched a near-genocidal campaign on the 'spacers. So the real question is what would a Freespacer want to be doing near Yamatai?
Why can't a Nekovalkyria be built in the United Outer Colonies and assist in their peacekeeping efforts?
Nekovalkrja bodies are pretty much weapons in their own right, and are treated as such in foriegn affairs. Any Valkrja outside Yamatai's borders without permission is subject to a Kill-On-Sight order.
Wouldn't it be possible for a Yamataian to immigrate to and Nepleslia have kids there, and then the kids decide it'd be a good idea to join their new homeland's military?
Yamtaian's rarely immirgrate to Nepleslia, usually it's the other way around for a variety of reasons, quality of living and what not. Currently there are no laws in place preventing children born by immirgrants to join the military, although nations like Yamatai sometimes frown on taking species other than their own (including other humans) from joining th military, and I have yet to hear about any other races forming ghettos there.
I'll leave a few brief notes for you to go through if you feel like going through them, they may help clear the situation better.
Nepleslia: Pretty much the stew pot of the universe, you can expect to find any type of species here if you look close enough. It's a rough place, so there's usually a bit of emigration to other factions (YSE and UOC). I believe there is at least one Freespacer, and possibly a kohanian (don't quote me on that) in their military plots at the moment.
Yamatai: Based loosely on Japanese culture, which is notorious for xenophobia, the Yamataians tend to take an odd view of anyone not an android like themselves, until recently there was actually a law preventing any non-Yamataians/Nekovalkrja from joining the military. You might find the odd Nepleslian trying to fit in as best they can, but it much rarer. Also note that any Valkrja outside Yamatai's borders without permission is subject to a Kill On Sight order.
UOC: A splinter state from Yamatai, things have been pretty quiet here, the faction managers are both in the navy and are extremely busy. I believe they're more open with inter-species diversity, however they have a few somewhat more rogue elements to them (The Lorath Matriarchy).
Independants: A hodge-podge of species, the variety is half the fun sometimes. This is where most Freespacers I've known tend to congregate. Favourite playgrounds include Nepleslian space and the now abandoned Freespacer territories.
Smaller Factions: These are usually too small to have other species as minorities, although there are plans for some of the "outer-rim" species to open of their own foreign legions of sorts.