Can two Nintendo DSI connect to one another without wifi?

Yes!

The Nintendo DS system (and that includes all the spin-off consoles such as the DSi) has a built in linking system.

It's utilised well with games like Pokemon, where you can trade with someone in the same room as you, or Mario Kart where you can race with eachother.

It is similar to the old Gameboy version of sharing with the 'Link-Cable' system. This is very similar, except there's no cable! It's much tidier and cheaper!

Wi-Fi is using the internet to access extras and downloads for your console and games, for example with Pokemon you can trade with people from all across the world, or with Zelda: Phantom Hourglass you can play mini-games with annonymous people on the other side of the planet.

Wi-Fi and the Wireless Play are different.

As for the 'same cartridge' thing, only SOME games require this, and some games use just the one cartridge. If you check the reverse of the DS game, it will have a symbol with two or more DSs and some little radio waves.

It'll say either 'Single Card Play' or 'Multi-card Play' and that'll tell you if you need more than one cart.

Single Card Play normally referrs to games that will share a mini game mode for others to enjoy, such as Phantom Hourglass, New Super Mario Bros and Diddy Kong Racing.

With Single-Card Play the one without the cart must connect through the main DS menu.

Multi Card Play is more for those games that would require you to save the experience of sharing, such as the Pokemon RPGs. When trading, you have to save the game, or else you'll mess it up. In the Mystery Dungeon Pokemon titles, you have to have a 'Team' ready to share with your other half, which means you having your own game.

These games will usually have the wireless connection modes available in the games themselves, not through the DS main menu.

As for distance that the two consoles can link, me and my boyfriend have connected from around 20 feet before, and I've connected and traded Pokemon to him whilst he was upstairs and I was downstairs, so cars should be fine!

Nintendo Dsi Wifi

Yes of course. My friends and I play DSi all the time, in the car or anywhere. You don't need internet connection at all.

YES, if you just want to play a game together, use download play

They do work without wifi. I'm sure they will have loads of fun :D

Yes, thats easily possible.