Traveling to Riyadh - help!

Hi,

I'll be traveling with my husband to Riyadh in 2 weeks. Can anyone tell me what is the dress code for women on the streets? Do I need to wear an abbaya? and the veil? We will be staying at Courtyard Marriott Diplomatic Quarter. He will be working but I will be by myself. Is it ok to be alone as a woman? Go to a shopping mall alone?

Also, we will need to get SIM CARDS, do you know if they sell at the airport? Is there a mobile carrier you recommend?

Thanks in advance for any advice you might have.

Daniela