I was in Saudi before. Everything is there in Saudi about what you are looking for. Life is little difficult for bachelor over there. You can go for shoping alone by taxi. You can ride in a taxi. You can go alone by taxi but you must seat back side not beside the driver. If you wanna take any man with you then he must be your hubby/son/father/brother(not cousin). Always you have to wear abhaya covering your head. Covering face is not mmendatory but ladies covering. As you are muslim, you will feel comfortable wherever you will go. Hotel, restaurant, bank every places there is seperate ladies section available. Weather is little dry then Doha. In weekend you can go to Makkah for Umrah.