Hawkeye--
Well, I can't shed much light on your questions, but I am particularly interested in the combination of Falco and Neon gobies. Here are my comments, for what they may be worth:
1) IME, you shouldn't have any problems other than the possible hawk goby issues
2) The shrooms should be fine if you have almost any kind of light at all
3) I have had emerald crabs and never had a problem, very fun to watch
4) About the hawk...Falco is smaller, so you may be fine. I have a pair of neon gobies in my display and a pair of longnose hawks that are just about done with QT. I have serious concern about the combination and may move the gobies to my sump to be safe. The hawks are too small (now) to eat the gobies in one gulp, but I have fed them a few small feeder guppies during QT and was surprised to see that they don't just swallow the guppies. They catch them "crosswise" in their mouths and take them to the surface and "shake" them for a while prior to turning them sideways and swallowing them. I am not sure what that is all about. The guppies are very small and could be swallowed, no problem. My concern is that even if they can't swallow the gobies (until they grow), they certainly could kill them by doing this catch and shake routine. None of this may be an issue with the Falco, but it is my experience with the longnose. I did have a flame hawk with the neons and never had a problem at all, but the flame hawk is much more peaceful and not known to be a problem.
Good luck!