If you have no orange liqueur, you can still make a very good margarita. It is called a Tommy's Margarita, it was invented in San Francisco, and plenty of bartenders prefer it: tequila, lime and agave, with nothing in the way of the agave itself.

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The one thing that matters
Agave rather than sugar syrup is the point. It is the same plant the tequila came from, so it agrees with the spirit in a way plain sugar does not.
Yes. Use two ounces of tequila, one ounce of fresh lime and half an ounce of agave nectar. It is called a Tommy's Margarita and many bartenders prefer it because nothing gets between you and the agave.
Agave nectar is the best answer and makes a genuinely different, cleaner drink. Cointreau is the upgrade if you want orange back. At a push, a splash of orange juice with a little sugar works, but it is noticeably thinner.
Cointreau is a triple sec, and a very good one. Cheap triple sec is sweeter, lower in alcohol and less orange-forward. If a recipe just says triple sec, Cointreau will always improve it.