To answer your title question: Yes, both Highway 1 and Highway 90 are under Israeli control. (As opposed to who?)
Originally Posted by
allset2travel
In other words, is it ok to drive on them by foreigners?
Yes
There are tons of conflicting info on the web (mainly blogs).
What blogs say you can't drive on them? I'm curious, if you could link some please.
Would Avis or Hertz let me drive a rental car on these roads?
Absolutely
Thank you if you can also point me to some official sources that confirm/not.
I don't know of an official source, because it doesn't sound like the type of thing that needs an official source. Looking at Avis's site, the only driving that is listed as forbidden is entering the Palestinian Authority.