like how many sockets can one have on a either ring or radial circuit planned to be protected by 20A breaker
The number of sockets you can have connected to a circuit isn't limited by the circuit breaker's amperage. No matter how many sockets you connect, you're still limited by the 20A limit on the circuit breaker. A socket with nothing connected to it does not draw any current.
Think about what devices you want to connect to the circuit. Find out how many amps each one draws and total that up. A 20A circuit can supply 20A intermittently or about 16A continuously (load for more than 3 hours at a time). Use the total amperage you need to supply to determine the number of circuits you need.
If you wish to connect multiple devices, but not use them simultaneously, you may do so as long as they don't exceed 20A or they'll trip the breaker.
"Ring circuit" suggest UK or a country using similar practices and regulations.
As far as I know, BS7671 allows for (or simply suggests) up to 100 m length of T&E cable covering a floor area of up to 100 m². There is no limit to the number of sockets per ring.
Typical UK homes have one ring per floor and a separate ring for the kitchen/utility rooms.
A 20A breaker is sized to protect the cable (so depends on cable cross-sectional area, not on number of sockets, and not simply on how much current you would like to draw) The breaker limits the total current draw through appliances connected to sockets.
So you could in theory have 150 sockets with 100 mA appliances running. Or just one kettle.
In the UK, adding sockets at new locations to an existing circuit is not notifiable but adding a new circuit (ring or radial) would be notifiable under Part P - so you'd probably pay an electrician to do the work and certify it.
Just to add to what rj said...you can only utilize 80% of a breakers rating. So if you have specific uses don't exceed the 16A or add another circuit to that. But as rj said...you are not limited by the number of receptacles unless the load is known. In my exp. many people put on about 8-10 per circuit. I personally split circuits by rooms, larger rooms splitting into more than one circuit.