To answer the first question, sorry I keep breaking it into smaller components but again, separating it out makes it clearer. If we look at:
what the IDF intentions are
what their actions are
what the effects of their actions are
What people think kind of depends on how well we think it matches up and whether we think the first one is actually an okay justification for the third one. Like when is it okay shoot when you can see there's someone in the crossfire.
What their intentions are
The IDF and mainstream Israeli politicians publically stated intention is to "destroy Hamas" in order to protect the safety of Israeli citizens both in Israel and in the part of Palestine that Israel is occupying. Hamas is a broad term encompassing both militant (eg militant) and civil (eg Health Dept) organization. Some politicians have gone a lot further and said their intention is to remove most Palestinians from Gaza. Some have said that no civilians are innocent, but these are minority viewpoints.
What their actions are
This is where it gets tricky, and some of it is contested. What is common ground is that they have chosen to use an unusually large number of bombs in a built up environment full of civilians, using huge bunker buster bombs, and drone bombing of targets suggested by AI. It also involves a ground offensive, and there appear to be "kill zones." The IDF has set itself numbers for "acceptable" number of civilians per kill, which may be high, and also permits itself to bomb hospitals and schools. Here is an article which covers some of the AI concerns. They also keep tight control of humanitarian aid and limit what enters. There are allegations that are disputed, of widespread deliberate killing of wounded and civilians and children. We may find forensic evidence in the mass graves. The IDF dispute it.
The effects of their actions
I've covered this already above, but what stands out is the unusually high number of civilians and medics being killed, compared to other modern wars that involved urban warfare. To put the total mortality into perspective, during the Bosnian Genocide 3% of the population were killed over a 2-year period. 1.5% of the Gaza population have been killed in 6 months. The mortality statistics we have are for known deaths, those still buried in rubble are extra.
Using satellite images of before and after, analysts estimate 57-60% of buildings in Gaza are destroyed, rising to 75% in Gaza City. We also know the hospitals were bombed.
During the current war monitoring of humanitarian aid entering Gaza has drastically reduced the amount going in. (Before this war, Gaza did not function self-sufficiently. A significant part of the population (many were refugees) relied on humanitarian aid.
NGOs on the ground report that the current numbers of starving people will meet the technical threshold for it to be designated famine, by May.
For many of those who are on the side of civilians, there is no possible justification for killing this many people to get to each millitant. International law (eg Geneva Conventions) specifies how to treat civilian populations, and many international experts think that these rules are being breached. Moreover, the blocking of humanitarian aid is problematic, whatever the rationale.
Most of us live in civilisations where we do not find it acceptable to kill innocent people as way to also kill guilty people.