Must they tell you that you can’t wish for more wishes before you start wishing? If you only have one wish and you wish for more wishes and they can’t do that have you used up your wish? Do genie’s only live in those oil lamps that look like gravy boats or could they be living in any kind of oil lamp? Any kind of lamp at all?
Various tales speak of genies in rings, as well.
De Camp’s The Purple Pterodactyl discusses genies in a modern context, and I recommend his work.
Why “need answer fast”? Ya got something going?
If you get three wishes, and ask for more wishes, you violate the 3 wish grant and you get nothing.
The number of wishes is immutable. That’s why the correct strategy is to wish for more genies.
If I recall, in the original Aladdin tale, there was a powerful genie of the lamp, and a less powerful genie of the ring.
In my experience, your best bet is to be friendly with the genie, offer her some beer, and ask her advice on the best way to use your wishes.
“Grant me more wishes, and I’ll free you after.”
Not only are they not required to tell you the rules, they’re perfectly allowed to lie to you, to trick you, and to set you up for failure. The nasty ones interpret your wishes creatively.
I want two tons of gold.
(You are promptly buried alive under two tons of gold.)
I want the lover of my dreams.
(You get the lover of your dreams…but she has leprosy.)
And, of course, the classic… “Okay, you’ll live forever. You’ll be a frog, but you’ll live forever.”
I’ve watched super-obsessive Dungeons and Dragons players try to craft a hyper-legalese “contract” that closes off all such loopholes. Masterpieces of creative logic-wrangling, but, ultimately, an Evil Genie can always win. He can sign the contract, screw you over, and just smile: “Who said my signature on a contract was going to be binding?”
Dopers make good Literal/Asshole Genies. 
Corrupted Wish Game.
Corrupted Wish.
That’s why it’s better to ask for a case of your favorite beer, season tickets for your favorite team (be sure to specify the year), and and a meal at your favorite restaurant. All but the most evil-minded genies would be impressed by your lack of greed.
My understanding of the jin, or genie is you can wish for more wishes - but there is a cost in doing this and the jin really won’t want you to. If you trap a jin the standard was to grant 3 wishes for the release of the jin. Done in this format as agreed would result in 3 and only 3 wishes which the jin would do honorably.
But if person would wish for more wishes, that would need to be allowed, however the jin will now seek other means of gaining their freedom. In this case the jin will (and has to) grant every wish, however the jin will take vast liberty with how you phrase your request to make it not what you wanted to the point that you then later agree to break the contract and set the jin free.
New hack
Jinns are creatures of fire. That’s why they have been trapped in lamps*. I assume the ones caught in bottles are sort of analogous to smoke. The Jinns trapped in a bottle only “lives” there in the sense that inmates live in a prison – it’s not their normal habitat. TV’s I Dream of Jeannie prettied it up. In the story of Aladdin, ones in a ring. Given their druthers, though, Jinns live anywhere they want – often out in the desert.
There’s no canonical rule about wishes. Jinn aren’t even necessarily required to grant wishes. If you’ll recall the Arabian Nights story of the Fisherman and the Jinn, the trapped Jinn originally wanted to kill the fisherman who released him, because he was so pissed about being trapped in that bottle for so long. It was only after the fisherman tricked him (“I’ll bet you can’t get back in that bottle”) and secured his promise that he got his wish.
As for how many wishes, and what the rules are, ever storyteller makes up their own. It’s not even consistent in the Book of a Thousand Nights and a Night, let alone all the fantasy stories since.
If you’re writing your own story, feel free to make up your own rules. Points for originality.
If you’ve found an actual genie, good luck. Watch out for lawyerly tricks and loopholes.
*…and not because they’re small, The Seventh Voyage of Sinbad notwithstanding.
There’s an episode of The X-Files that riffs on this, “Je Souhaite” (French for “I wish”), written by Vince Gilligan. Gilligan must have known such obsessive D&D players (or maybe been one himself). After seeing a succession of owners get disastrous results from their wishes, Mulder gets control of a jinn (named Jen, of course). Trying to be selfless, he wishes for world peace. Everyone on earth except him immediately ceases to exist. As Jen points out, wanting to be “the man who brought about peace on earth” is not a selfless desire.
He uses his second wish to undo the first one. Then he spends hours attempting to write the perfect third wish, trying to be incredibly specific so as to avoid all potential problems. Finally Scully convinces him that this is all for naught, so he uses the third wish to set Jen free.
Jen, incidentally, claims that she was made into a jinn by another jinn 500 years earlier, when she foolishly wished for long life and great power.
I’m not sure where the 3-wish standard came from. In the original Alladin tale, the djinn was the perpetual slave of whoever was holder of the lamp or the ring. Other 1001 Nights tales mentions djinn imprisoned in brass bottles, but opening the bottle simply let the djinn take off to parts unknown.
So this cowboy is riding across the range, and suddenly his horse spooks at a huge snake, rearing up and almost throwing him off. He pulls his six-shooter and prepares to drill the snake when it speaks up: “Wait! I am a powerful jinn enchanted as this snake. If you spare my life, I will give you any three wishes you desire!”
So the cowboy thinks, and he says, “Okay. First, I want a body like Arnold Schwartzenegger in his prime. Second, I want the face of George Clooney at 30. And third, I want to be equipped (heh, heh) like my horse here.”
The snake says, “All your wishes are granted. When you wake up tomorrow, you will have all these qualities.” And it slithers away at top speed.
The next morning, the cowboy sits up in his bedroll to find himself muscles on muscles. He grabs his shaving mirror, and he’s so handsome he half falls in love with himself. Then he shoves the blankets down… and screams.
“Oh, my god… I forgot I was riding Nellie yesterday!”
Tim Powers had a great deal of fun making up new rules in his fantasy Cold War novel Declare.
I once published (small press) a story about a Djinn, and got a number of letters complaining that I’d made him too “rock-like” and not enough “flame-like.” Yes, my Djinn was pretty much a mineral elemental…but I was, as you say, making up my own rules. People are really strict with their expectations!
(A friend of mine gripes at vampire movies and books these days, snapping, “These aren’t real vampires!” Right… Because we have such a good collection of facts and data regarding the behavior and physical properties of real vampires…)
I don’t see any way to screw this one up: “I wish that you have to grant the intent of my wishes, to my satisfaction”.
P.S. What was the short story where a logician figures out a way to turn three demonic wishes into nigh-limitless power?
Anybody want to buy this wish-granting imp in a bottle from me? Only one cent…