Lilmod: Based on your standards, I would rather have a “non frum Army” who is worried about being court marshaled than a frum one. Don’t we have the parsha of Isha Yefas Tohar? This gives a blanket waiver to any soldier to capture, rape, and even marry a non jewish woman captured in battle.
Imagine the outcry from the frum communities if the Israeli army did that in 1967 to the Arab women?
The point of a Jewish Army is to protect the land of Israel, not the Torah. The rabbanim and sanhedrin are the Jewish army for protecting the Torah. No where in our history was the Jewish army ever required to follow the rabbonim. In addition, throughout our history, a large part of our army were mercenaries starting back from Dovid (maybe even Shaul) and on.
An Israeli army would have every male eligible drafted in the army. In your downtime, open a gemara and learn. Not even in today’s Israeli army do they stop someone from learning on their downtime.
Yes, they will need to work on Shabbos.
When moshiach comes, they can put down their guns and go back to learn, which I doubt as the gemara in Shabbos discussed if the soldiers would be allowed to carry a sword on shabbos once moshiach is here. So it seems that even then we would need an army.