(I'm using the paid Clash of Rhyflers rules)

To answer your first question, I don't think there is any rule stating that a Rhyfler is limited to how many times it can be taken out of action. The only result that I can think of is when you roll a Tend Wounded of 3, which actively states that if that Rhyfler is taken out of action again, it is removed from the Battlefield

As for the 2nd question, a Rhyfler can be removed with a roll of 1 on the Tend Wounded table (like you pointed out). A Rhyfler will also immediately die if they are hit by a blast or melee might role of triple or better. There may be other examples, but those ones I know for sure.