Do women or you have to cover up?
Dress as you wish, but be respectful of the culture here. Omani women dress in many ways: with embroidered abaya (full length, long sleeve covering) and headscarf; jeans, blouse and headscarf; no headscarf, etc. Any way is fine, though the traditional and customary way is with a headscarf. Below the knees, below the elbows and loose fitting seems a good rule of thumb for Westerners, certainly during business hours. On the beach on the weekends, though, I've seen plenty of shorts and T-shirts on Westerners and the rare cropped leggings and short abayas on women.
Omani men and women working in public offices have to wear a certain outfit/uniform: women wear the abaya and scarf and men wear a white dishdasha (floor length tunic) and a sort of turban (muzzar). A tassel hangs off the right collar of the men's dishdasha, traditionally this was dipped in perfume. On more formal occasions the men will add a sash of the same fabric as the headwrap and a long black robe, open at the front.
Can women drive?
Anybody 18 and over with a license can drive.
Can women go out alone?
Absolutely, though a young single woman wouldn't go without a brother, cousin, or other women to the movies, to a restaurant, to a party unless it were a family event.
Can you buy alcohol?
Yes, if you are 21 or older at licensed bars and restaurants, mostly in hotels. With an alcohol permit (easily obtained from the Royal Omani Police) Westerners can buy alcohol at specially licensed retail stores. Additionally, you can bring a limited amount with you when you fly into the country. There's even a conveniently placed Duty Free store on the way from Immigration to Baggage Claim!
What's the food like?
Middle Eastern (think Lebanese-style) and African and Indian influenced. An Omani restaurant I've been to several times (Kargeen) features grilled meat, marinated meat baked in palm leaves, and a variety of flat breads. Restaurant cuisine varies widely in Muscat, with offerings from Italian to Indian, Mexican to Chinese and several in between. Even the cupcake fad has hit here. There are also plenty of American chains all over (Starbucks, Subway, KFC, Baskin Robbins, etc.).
Answers to the questions commonly asked by Omanis:
Where are you from?
Where are your parents from?
My mother is from Hamburg, my father was born in Valencia, Spain.
How is your mother doing?
Very well, thank you.