You can take pictures. But you are not allowed to take someone else's picture without their consent. Nor you can take pictures/ videos of the places without the approval from the higher authority.
Yes, Dubai & Abu Dhabi are safe places to visit. They have CCTV cameras to monitor & provide you with safety.
According to the Government guidelines, you are not allowed to kiss or hold hands in public places. Whether you are married or not, kissing is strictly prohibited. Neither, unmarried couples are allowed to stay in a single room.