When playing a mutant do you get more mutations when you lvl up ?
As covered, you can buy a new mutation if you save up enough mutation points. You can also choose the Unstable Genome at character creation and get a 33% chance each level to choose a new random mutation from a selection of three. Presumably this will happen once per the number of times you took unstable genome. It is not very efficient, since it costs 3 of your starting 12 mutation points to select each Unstable Genome, but I suppose you can get lucky and get to choose an expensive mutation (like Regeneration or Force Bubble, which cost 5 each) for cheap.
So. I've encountered a twining lamprey. How exactly do I, uh....make it stay dead?!
Kill both partners in the same turn. Get creative.
I have repeatadly risked point-blank suicide grenading on them, and it hasn't worked.
Use a stronger grenade. Baring some bug that you might have, you pretty much have to kill them both in an explosion. Since they keep pace with you quite easily it's tough to get to a safe distance to use it. Maybe if you have some reliable way of stunning or freezing them you can try that: bring them low, freeze them, hope they don't unfreeze while you kill the one, and hope the other doesn't unfreeze while you kill it. But I don't know if it'll work; they're not affected by my sleeping gas, and I haven't tried many of the esper powers.
Remember to bring both of them to low health before you blow them up: both at badly wounded if you can manage it. If you accidentally kill one while trying to whittle it down, just try again on the fresh spawn.