90 days in Israel

Under normal circumstances, a 90-day visa will be issued whenever you cross into Israel. The visas normally are not multiple entry, so if you leave the rest of the 90 days is not longer applicable and you'll be issued another visa when you enter Israel.

It is possible that you could be denied entry by Israel, but it is unlikely unless you've been up to any suspicious behavior in the Middle East.

#1 is correct. There are no set rules limiting your time like there are in Europe for example. Every time you enter Israel you'll normally get a new stamp valid for 90 days.
However if you keep leaving on day 89 just to re-enter the next day, then border police will start to suspect that you are not a bona fide tourist and will refuse you entry.

Thanks to both of you! My aim is to spend four months in Israel, for which I would need to exit at least once. Would this be all right? Also, I was in Algeria for three months, volunteering, Do you think this might cause me trouble?

There is no problem doing e.g. a side trip to Jordan as long as you aren't clearly staying longer term. Algeria might be cause for a couple of extra questions, but if its the only "suspicious" stamp in your passport it's unlikely there will be any problems.