How many of those protests are about Palestinians?

The vast majority of them, and the largest of them, are about saving the “hostages” and opposing Netanyahu.

One of the largest protests so far: https://www.thejc.com/news/israel/israelis-protest-gaza-war-netanyahu-wftw9xpj

Not a single mention of Palestinians.

Speaking ahead of the rally, Yehuda Cohen, father of hostage Nimrod Cohen, accused Netanyahu of “blowing up the hostages in Gaza.” He stated: “Netanyahu is killing the hostages and destroying the country.”

“The hostages’ lives are in your hands, time is running out, the hostages have no time. We’ve seen hostages return. You have the power to do this. So please do it already. Sign phase B and bring my brother back to me. Give me my life back, now!"

The surge in demonstrations was also partly triggered by Netanyahu’s move to dismiss Shin Bet chief Ronen Bar and Attorney General Gali Baharav-Miara.

“The government has launched a direct, violent and unrestrained attack: on us, on our democracy, on our values, on our future, and on the lives of our children. It will not win,” he went on, accusing the government of “turning its back on the law, on the High Court of Justice and on the public.

“This struggle is not another protest. This is a struggle for the face of Israel. This is a struggle for our home,” he implored.