Let's say I want to develop a small filmmaking game, which include real celebs names and photos. Would it be illegal to do without actually permission of this celebrities? And how properly ask them for permission and don't get in law issues, when game actually come out?

It depends on the country. In the UK usually yes. In the US most likely no. But like Ashaman says consult a lawyer.

I wouldn't want to risk such a thing, even if my lawyer told me "sure, no problem" (though most likely, he will only say "it depends" anyway, lawyers don't like giving clear answers or committing to something).

Using a dead person's name or image might work in some countries (but, with different waiting periods), but as far as living people are concerned, this is outright asking for trouble.

Also, not few celebs have a mark on their name, which doesn't automatically expire if they die (but passes onto heirs).

AFAIK, If you create a parody, you might get away with it (google "fair use")....

Else you will most probably need the celebs approval. Which might not only mean getting in touch with them or their managers, but also paying something for the privilege of using their "brand".

But as others said, it depends on the country (of the celeb, where you do business, where you live... if its illegal in one of them, you should avoid it anyway), and get a lawyer involved, as the internet is a bad advisor when lawsuits are a potential fallout of a wrong decision.

Let's say I want to develop a small filmmaking game, which include real celebs names and photos. Would it be illegal to do without actually permission of this celebrities? And how properly ask them for permission and don't get in law issues, when game actually come out?

Who took the photographs? The photographs themselves are works of art and automatically copyrighted by the person who took them. See the Hope poster lawsuit. Personally, I think the Hope poster was fair use; it was significantly transformative in my opinion. But the case, costing money and time, was too much of a nuisance and was eventually settled, costing more money.

Faces? Celebrities make their livelihood off of their faces and names in addition to their actual skills - there's extra protection for them.
Just using the name "Matt Damon", "Johnny Depp", "Will Smith", or etc... increases the likelihood of success of a major movie. It's serious marketing.

See Right of Publicity:
"By the broadest definition, the right of publicity is the right of every individual to control any commercial use of his or her name, image, likeness, or some other identifying aspect of identity, limited (under U.S. law) by the First Amendment. [...] Because the right of publicity is primarily governed by state (as opposed to federal) law, the degree of recognition of the right of publicity varies significantly from one state to the next."

EASports got sued for trying to put college football stars in their sports game without actually using their names. Instead, they used jersey numbers, statistics, what college they attended, and so on, trying to gain the benefits of having the celebrities without actually using their name. They toed too close to the line, the lawsuit was filed, and probably fearing that they might lose, EA settled.

Celebrities make their money off of using their names and faces. Like EA, you want to benefit from using celebrities without actually paying them. They won't be happy, and they can sue you, and even if they lose, it'd cost you time and money and hassle and lost sleep.
Anyone can sue you for anything, it doesn't mean they'll win. But here, you're waving a flag with specific peoples' names on it, saying 'sue me'. And the people who're going to sue have deep pockets, plenty of lawyers on retainer, and are used to defending their right of publicity because it's their whole business model.

Invent your own "celebrities" - be creative!

The direct answer to the question is in the Forum FAQ and the sidebar, here is the direct link. Original Poster (and probably a few others) should read it.

For those mentioning parody, that does not apply to this situation. Parody is about using a thing in an unexpected way in order to make a statement about that thing, and it requires using the minimum amount necessary to make that statement. Displaying Mario in his world in order to show that he was actually terrorizing Bowser's kingdom, invading and destroying, and Princess Peach was actually in a peace conference with King Bowser, that can be a parody. But "a small filmmaking game, which include real celebs names and photos" is not a parody no matter how you try to arrange it. Even so, it is an affirmative defense, more on that below.

For those mentioning fair use, that doesn't apply here either and is also an affirmative defense. Generally fair use requires minimal use, typically just enough use to make your statement about the thing. Fair use has different definitions in different locations, but is typified by educational use or news reporting or social commentary, quoting just enough of the material so you can make the point. Again "a small filmmaking game, which include real celebs names and photos" is not among the fair use exemptions. Using it on the evening news or giving the name for an education textbook would likely qualify.

And both are affirmative defenses. That means you are claiming "I am infringing, but this specific use is immune because...". It is a high risk legal defense. You still have legal action against you, you still need to hire a lawyer to help defend you. Even if you win at court, in nations where fee recovery exists an affirmative defense usually doesn't qualify for fee recovery so you are stuck with the bill. And if the judge disagrees with your exception, you have admitted to infringement.