"stand its ground" not "stand our ground" (this is a select from the words provided exercise)
Yes, that sounds perfectly fine if it's "we stand our ground". However, "our battalion", regardless if you're actually in it, is a third-person noun. Hence why it must be "our battalion stands its ground".
What if the leader of the battalion (so, a person part of the battalion) was talking with the enemy battalion leader. Should he/she use "its ground' or 'our ground'?..perhaps, my battalion will stand it's ground?
This is simply a difference in how people perceive the point of reference.
"Our friend will stand his/her ground" vs "Our friend will stand their ground". Both are correct.
"Our battalion will stand its ground" vs "Our battalion will stand our ground". The latter just provides more emphasis on "the ground/territory" aspect.
This is not a good example. We use their to refer to one person when the gender of that person is unknown. So if it is a friend then we will use he or she because we know "them". See how it works?
It depends on how you're looking at it.
"Our group will patrol our land" (more emphasis is given on the land) or "Our group will patrol its land".
The battalion is a singular thing, not a plural. We stand our ground, IT stands it's ground
The only correct one is "our battalion will stand its ground". The subject is the battalion, not us.
You could argue it can even be "our battalion will stand their ground". It's merely a matter of different people processing the noun as a different. In the case just given, it would be more for when you and/or some others are part of the group but not within immediately vicinity of the rest and when you consider the battalion a collection of individuals rather than just a single unit.