I think the question is an easy answer.
Yes. Israel has nuclear weapons. Its stock is estimated to be at
100-200.
Israel does have the right to have nuclear weapons. Firstly, every
country has the right, provided that the country did not sign the
Non nuclear Proliferation Treaty. Thats the legal part anyway. The
fact that many Jewish scientist migrated to Israel after WWII
accelerated Israel's efforts. Note, the grandfather of the nuclear
bomb, Einstein is a Jew as well. Many critics claim that he was the
one who gave Israeli's the know how.
Next, Israel's nuclear capability is a stabilising factor in the
region. The ceasefire of the Yom Kippur war in 1973 can be partly
attributed to the fact that Israel has a high possibilty of
launching a nuclear strike.
If you have not realised, there has not been a single war involving
Israel since 1973. If any Arab state wish to attack Israel, they
must assume that Israel will retaliate with their nuclear arsenal,
which no state can afford to.
Thirdly, Israel is a sovereign state and has the choice to pursue
any defence or foreign policy it desires to. Any analyst will tell
you that in most cases, US have no leeway on how Israel acts. In
almost all instances, US was dragged into the foray to support
Israel as US requires Israel as a check and balance instrument
within the region and can not afford the death of the Israeli
state. Thus the Israelis leverage on that fact and acts rashly
sometimes, knowing full well that US have to back them. You should
also realised that Israel has been warned or threatened many times
by the US for its rash actions.
I hope this can answer most of you guys queries regarding Israel's
nuclear capability.