Pakistan does not recognize Israel (not sure if vice versa), so Pakistani citizens cannot travel there.
However if a Pakistani holds an European passport as well, can s/he travel to Israel for visit without having any problems at immigration? Also do they mark the passport with any kind of stamp as that would certainly cause problems on arrival to Pakistan.
Though Pakistan itself is not mentioned, recently an Israeli newspaper published an article on Muslim and Arab tourists in Israel.
More than 250,000 Muslim and Arab visitors from countries which have no diplomatic relations with Israel have arrived in Jewish state since 2009.
Most of the tourists came from Indonesia and Malaysia, which have no better relations with Israel than does Pakistan. I've personally met and enjoyed an afternoon on the Dead Sea with a family from Saudi Arabia. When I specifically asked them how the typical Israeli Jew treats them, I was told that they are treated better in Israel than they are in any European or Arab country that they had ever visited.
Regarding the passport stamp, Israeli immigration can stamp a form outside your passport for you. This is commonly done, just mention it to the immigration officer as you pass him your passport.
Yes. You can, but it is not certain.
Israel does welcome tourists. For three months.
That said, Israel known to have very tight security, especially around airports and borders. You should be prepared for prolong security interview upon arrival, and could be prevent entry to Israel if the security personnel have any doubt about the purpose of your visit.
To increase your chances, I would recommend for you to get the visa before arrival, make very sure you have all required documents for B/2 Visitor Visa and disclose any information when asked.
Disclosure: This written from personal interaction with individuals that visited Israel in the past. I do not work or associated with Israeli airport.
As answered to the question Is it possible to travel to Israel if it's not recognised by your passport's country? Israel allows citizens of all countries to enter its borders, as long as they have an appropriate visa. There are countries for whose citizens Israel doesn't require a visa for a tourist stay of no more than 90 days. Pakistan specifically doesn't recognize Israel and doesn't have diplomatic relations with Israel and is not on that list so a Pakistani citizen would need to acquire a visa prior to their visit to Israel.
For a european citizen the procedure is the same, even if they are a citizen of non exempt country, like Pakistan, as well, if they are from a country that is on the list then they can travel to Israel without a visa for a period of up to 90 days for tourism purposes. If they are from a country that requires a visa, then they need to acquire a visa before their visit.
If you plan to visit Israel with the Pakistani passport, you best contact an Israeli embassy and ask them about the needed procedure to acquire a visa, also, you would probably want to make sure that the visa will not be put inside your passport, as it may lead to problems with Pakistani authorities.And as noted in answers to other questions on this site, Israeli border control doesn't stamp a visitor's passport. This permits the the passport to have no record of the visit to Israel.
The closest Israeli embassy to Pakistan is in India, but a visa can be acquired from any Israeli embassy around the world, no matter the residence of the person applying.
One last thing, Israel, like all other nations reserves the right to not admit citizens of other countries to its borders for various reasons, people who come from enemy states, or states with no diplomatic relations, like Pakistan, are obviously more suspicious to Israeli security agencies, if you come to Israel using your European (or other friendly state) passport and are asked by the authorities about other citizenship, it's best to tell the truth and be forthcoming, trying to hide such information may lead to high suspicion and denial of entry.
