Well, the only place you really see it would be the demigod selection game. Ingame you'd hardly notice anything as you're well zoomed out. and she's occasionally hiding in the plant bulb.
Nukaen
I had that problem earlier today, tried again immediatly afterwards, and it worked. So I just shrugged it off as a fluke.
Not sure where I read it, but I'm pretty sure the death penalty is just the time lost. Might actually be for the tooltip for the countdown timer when you're dead, though, I'm not sure. About Pantheon, then no, there's no way to play an arranged team in that, which is partly the point I guess. but yeah, would be nice if you could form a party with friends :X
About them being dependent on the demigod you've chosen - try to pick an assassin demigod :P It's dependent on demigod-type and not unique to specific demigods per say.
I'm just guessing now, as I don't know the mechanic. But as the pantheon is about gathering a set amount of points - then it will end at some point. And presumably you can take a new side when a new pantheon starts. But yeah, this is all speculation from my part, and as I don't have the game (yet), I can't say whether or not I'm also stuck with a side or not D: