Dont you get extra turns from extra agility? tooltip seemed to suggest you did.
Anyhow, I find that you can run out of stamina fairly quickly so it´s not a waste either case... but TBH the stamina increases are nothing to write home about either.
(Everything here is based on an older version on medium difficulty, and the current version on easy... and based on my reading of the patch notes, Medium was made mostly easier too.)
You can, but it's pretty slim. From my understanding of it, which I totally do not guarantee accuracy, AGI regenerates Speed, it costs 100 Speed for a turn, and turns are taken in the order of most to least remaining speed, so somebody at 119 speed that generates 20 speed per tick would move before somebody generating 40 speed per tick but is only at 110... but the guy generating 40 speed per tick would get the next turn first. (Assuming I didn't botch my numbers... didn't bother checking validity.) The difference is so small that getting like one extra turn out of 15 is practically invisible... it's more important to just make sure that you have just enough that you won't have a key unit repeatedly bashed against a wall until they die.
The stamina gain is actually a bigger deal, I'd say, but it's kind of breakpoint-y. I don't remember off-hand, but something like 25 points is enough max stamina for an extra ranged assist from a crossbow or javelin. 10 points or so is enough for an extra hit if you use that trinket that prevents people from moving past you.
Starting the 30th day (I think it was increased to 50 in a recent update), there's a squad that chases you around the map that's aligned with the group that mutated you to begin with.
I'm not sure what happens if you fight it off as I'm away from my desktop and I haven't had to deal with it on my laptop save yet. You CAN fight it though, and it's not an overpowered impossible battle. Edit: It's pretty easy on easy. You get generic battle rewards, which considering most battles have some kind of extra reward, means it kind of sucks.
I find the VIT and STR balance is mostly dependent on how many trinkets you use and how effectively you utilize a priest, if you use one. In a big battle, you'll basically be able to cast 1.5aegis a turn, or maybe 1aegis+2lifedrain, which cuts down on VIT requirements. And non-frontline priests are good place to pump CON... the starting trinket, Last Stand, is really useful and you can combo it with a priests high rate of special generation to begin with, lack of other necessary stats (STR is lousy on it to begin with and Lead doesn't depend on its own stats, it doesn't have much that synergizes with AGI like the rest, and VIT never hurts, but you can just keep it a few steps back from the frontline to begin with), on top of that trinket that lets you start off with your special precharged 2x. Unless you get some really good mods for your specials though, CON is a dump stat too. So enough AGI to keep at parity with your enemies (or a tiny bit more), CON if you use your specials, VIT/STR as necessary.