It seems that UAE is literally nothing but high rises or skyscrapers (basically the same with Bahrain, Kuwait, Saudi Arabia or Qatar) while Oman has none of that (since most of the infrastructure is marble white or using bright colors contrasting the sun), though they’re on an even playing field when speaking about their wealth. Is it because Oman has a different approach on how they spend their money or retain cultural heritage?
You would be safe in almost all places. There are some places I wouldn’t go to alone when you’re a woman but that’s true in almost any country, and those aren’t tourist places anyway.
The only place you would be required to cover your head is when visiting a mosque. I would advise you to dress somewhat modest when you’re out and about, i.e. covered stomach, shoulders and upper legs. Not because it’s mandatory but because the locals appreciate it when you adjust to their customs. Bikinis and such are fine on private beaches of hotels.