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It seems like a battle that is impossible to win. Besides the ridiculous high HP and defense, the battle seems to end automatically after a certain number of rounds.

Yes is not a real battle, is really impossible to win against them in their own realm
About Rowinda, wait until the end of game... after the credits...
p.s. added spoiler tag!

Show me their nightmare stats and tell me how many rounds I get (and how they are measured - actions by the demons?).

Jul has 5300 health and you get something like 15-20 rounds of combat. And your team will be Althea, Jariel, Chalassa, Rowinda.

Oh, and Jul still has her healing attacks.

Lol those aren't real battles, but designed so that are impossible to win. No challenge possible at all!

I felt like a fool when I realized I just wasted my bombs and potions when "fighting" Jul.

Well you as a player might have wasted your bombs, but think of it from a character aspect. In what said character thinks is a do or die situation and the course is not going well, they certainly well would not hold back on the bombs.