Yes, but aren't the majority of Jews in Israel secular? Hell, they even eat bacon.
Ultra-Orthodox Jews do not serve in the Army.
I think that the Haredi soldiers have their own battalion in the IDF.
That all depends on what ultra-Orthodox definition you use. I don't believe there is a legitimate definition to support your case. The only one that fits is where you define ultraOrthodoxy by the refusal to recognize the State of Israel or serve in the IDF. That definition falls short.
Ultra-Orthodox Jews do not serve in the Army.
Is Ultra-Orthodox the same as Ultra-Right-Wing? And in about the same percentage of the population (i.e., < 1%)