Hiya,
Well, the public transport here will only take you in-between the larger towns, from Mct to Nizwa etc...there is no public transport in Muscat, only taxis etc.. so unless you do what Kruz did, 'rent a guide with a car' - you are stuck in the Muscat area.
Prices...well...you can rent a car for hmm...US40+ a day... taxi drivers tend to prey on tourists and going by taxi the whole time, you will most likely end up paying a lot more each day (especially in Muscat) unless you speak Arabic and is willing to spend a lot of time each day to haggle with 'em...
I assume you are all talking about diving in the area around Muscat....the best dive sites are the Dimaniyat Islands, lots and lots of fishlife - big and small... the only dive center going out there every day is Daymaniyat Divers located at Al Sawadi Beach Resort. If you use the dive centers in Muscat, it's quite a long boat drive...
In and around Muscat, there are only two dive sites worth visiting - the Al Masannah wreck and Fahal Island.. but then that's my opinion...
Malene, there is no need for you to cover up - what we recommend to our visitors is 3/4 length for legs (ie no shorts or miniskirts - you will however see women wearing this in Musat and the omanis don't really appreciate it...) and as long as you cover your shoulders (no tanktops) - you will be fine... if you are at a dive center or resort, you can wear whatever you want..
You don't have to cover your hair at all.
Unless you visit the SQ Mosque, then you have to be completely covered - hair, ancles, wrists and they do have guards denying you entrance if you haven't...