As far as Israel and nuclear research and weapons testing goes it is a know fact that they are doing nuclear research.
see:
Nuclear weapons and Israel - Wikipedia
Israel began to investigate the nuclear field soon after it
declared independence in 1948 and, with French co-operation, secretly began building the
Negev Nuclear Research Center,
[d] a facility near
Dimona housing a
nuclear reactor and
reprocessing plant in the late 1950s.
As far as nuclear weapons, Israel does not admit they have nuclear weapons.
Now it is speculated that Israel tested a nuclear weapon; see the Vela Incident information at :
Vela incident - Wikipedia
The
Vela incident was an unidentified double flash of light detected by an American
Vela Hotel satellite on 22 September 1979 near the South African territory of
Prince Edward Islands in the Indian Ocean, roughly midway between Africa and Antarctica. Today, most independent researchers believe that the flash was caused by a nuclear explosion
[1][2][3]—an undeclared joint nuclear test carried out by
South Africa and Israel.
[4][5]
The cause of the flash remains officially unknown, and some information about the event remains
classified by the U.S. government.
[5] While it has been suggested that the signal could have been caused by a
meteoroid hitting the satellite, the previous 41 double flashes detected by the Vela satellites were caused by
nuclear weapons tests.
[6][7][8]