Israel (now broader Mid East discussion)

Naturally, WhoDatPhan78 might (quite rightfully) argue that this leaves aside all of the very relevant arguments about what Israel could/should have done prior to October 7th to avoid this whole mess, and what Israel could/should do in that same space after they achieve their "objectives". But however right that argument might be, it doesn't deal with the present reality. Which, again, is why the details of messy things like rules of engagement are important, and why I asked the question in the first place.
Right. But then we should be looking at international human law, and the principles of proportionality, distinction, and precaution, which are what - at least nominally - cover this. Which is more of an essay type question than it is a simple and very broad "what are they allowed to do," question.

As I'm not, hopefully understandably, going to write an essay on this myself, I'll link to one, from Médecins Sans Frontières: https://guide-humanitarian-law.org/content/article/3/proportionality/

To the point, and to address part of your comment, I would agree with the statement there that trying to use "the overall strategic objective of its war to globally justify the alleged proportionality of massive civilian deaths and destruction" is wrong.

Edit to expand on that a little as I've got a moment: Specifically, I think it's wrong both as a general principle - I don't think what clearly qualifies as a war crime in itself can be categorised as not a war crime on the basis of nebulous broader objectives and asserted future outcomes - and I also think that specifically, it's wrong in its own terms. That is, to boil it down to its essence, it's an "the ends justify the means" argument, but in this context the means will not lead to those ends. It's a conflict driven not by a few individuals, so it's not one that can be ended simply by killing those individuals (at whatever cost), it's a conflict driven by a long set of complex factors including survival, retaliation, anger, hatred, oppression, resistance, etc., etc, etc. The 'means' here, in terms of the actions of the IDF and the cost associated with them, seem far more likely to feed that and drive future conflict, not starve it and reduce it.