Is rock garden suitable for drain off area where soil remains moist a lot?
Most rock garden plants like drier conditions. If you have an area that collects water, you may want to consider a rain garden. Here is information about that: https://www.gardeningknowhow.com/special/spaces/rain-garden-design.htm
I want to start a rockery in my garden. Can small stones be scattered around the plants without putting down membrane to stop weeds growing?
You can do this, but you will have to take extra measures to stop weeds from growing. Boiling water is a great natural weed killer, as is vinegar. Just avoid getting these on the plants that you intent to keep alive.