UK Is this ok to extend a ring main?

Yes, that is basically right.

Feeding the shed via a 13A FCU is perfectly OK providing that is enough for anything you need out there (e.g. couple of double 13A sockets for garden tools or the like). As it is most likely used outdoors, that circuit must be RCD protected, but probably your ring final already is.

For any lights in the shed use another FCU with a 3A fuse to switch and protect the cable, fitting, etc.

Just take care behind each FCU for what is on the supply side and what is on load side

It's probably a good idea to have an isolation switch (double poled) for the shed as well a as fuse. Makes it easier to isolate there's a problem.

Generally I use the MK Logic Plus range, they seem to be double-pole switching.

But never the "MK essentials" as they are rubbish!

The Scolmore Click Mode FCU are also Double Pole and have nice clear terminals for IN and OUT (as do the MK)

I'd avoid the cheap FCUs as the terminal layout can be confusing and fiddly to terminate. Whether you are going surface box or back box, 35mm will make things a lot easier in terms of space for a ring and a feed out.

For future reference, you likely won't want to run armoured cable directly to a fused spur, but via a separate adaptable box with room for the gland to be made correctly to ensure the armour is earthed (though I would always suggest using 3 core armour too)

(You could in theory gland SWA directly to a plastic back box, but it's likely to be an exercise in frustration without experience)

As always when breaking into a ring, you will want to ensure that you maintain continuity of each conductor and ideally have some way of testing that.