sorry am from Kuwait i do not about Qatar laws i came only as a tourist

As long as they aren’t busy working

Skirt and dresses could be acceptable but had to be the lenght of the knee, otherwise you can pass a uncomfortable moment. For men the dressing code is more relaxed and a short is acceptable. For women I recdomend long dresses, discret dressing just to avoid bad moments.

Ahora es buen momento para visitar Qatar. Hasta el mes de abril el clima es agradable. A partir de mayo puedes encontrar días muy calurosos, pero Doha de noche sigue ofreciendo veladas agradables al aire libre hasta el mes de junio. A partir de octubre de nuevo se puede disfrutar de paseos por la Perla al atardecer. En diciembre y enero en la Perla se puede pasar frío y lo digo por experiencia.

My answer got chopped off. above. I agree with the first responder. Also riding and walking are typically only activities within locations in Doha - not between them. Non workers dont usually do anything that makes them sweat or do anything "physical" - its a local custom. So walking and cycling are not high in the list of civilized activities. They are mostly dangerous.

Evening is the best time to visit.

depends what you want to do , look around the marina bit with boats and a few shops or go to kempinski hotel or one of their restaurants

actually I didn't try by water always by car but u can get boat from katara to take you to pearl.

No ticket needed in order to visit the Pearl which is an artificial island full of shops, restaurants and cafeterias!