There is no uncontrolled airspace in Israel, everything is class D or C. By default, R/T language for VFR flights is Hebrew, but controllers will switch to English on request. For IFR, it's English by default.
If you want to convert your JAA ATPL to PPL, you will have to sit an air law exam in Hebrew (no English version is available) and pass a skill test. I was told that on a foreign license you can only fly IFR, but I could not find a clause in the documents saying so. Maybe it's actually a language issue. Actually, the legislation in Israel is generally much less clear-cut than in Europe: if the law says you cannot do something, you may often be allowed to do it as a matter of exception if you petition the relevant authority and explain why you need it.
Israeli AIP is freely available for download, but the domestic part is in Hebrew only. International AIP (i.e. for IFR flights) is bilingual. IFR airports are LLBG, LLSD, LLET, LLOV (no private flights) and LLJR (seems to be closed, it's on Palestine-controlled territory). LLHA is international but VFR only. There are about a dozen more domestic-only airfields, but the information is somewhat in disarray: a visit to a few of them revealed some discrepancies. For example, LLYO is listed in the AIP as an active aerodrome, but the person in charge of it at the town hall of Yotvata (where it is located) told me it was closed. Apparently, it's legally open but unattended. There are also several aerodromes with known ICAO location indicators and seemingly some traffic, but not listed in the AIP (maybe they are for ultralights only?)