Re: when ready for slaughter...
If you're eating them yourselves, then they're ready when they're fit and big enough for what you want. You can grow them on as long as you want, depending on how big you want your joints - but watch they don't get overfat.
If you're selling them in the ring or deadweight, you get the best return per kilo if they will kill out at not more than 21kgs. For a very muscley type, like a Texel, this would mean 40kgs liveweight (with an empty stomach - up to 43kgs on the farm.) Hill breeds can probably go up to 45kgs plus (empty) and still hit the mark.
You get less per kilo, and often less per head too, if they are over 44kgs in the ring (46-47kgs at home.)
Just as important as weight is condition. They want to be fit not fat. Test the tail-head - run your fingers down the sides of the tail; if you can feel the tailbones easily, they're not ready yet. If you have to really squeeze the tail to feel the bones, they're too fat. Do the same on the loins and behind the shoulders, you should be able to feel the 'transverse processes' (where the spine juts out and the ribs attach) with pressure - but not too easily.
Age is irrelevant, except if they get old enough to start cutting their adult teeth, in which case their value plummets as they cost more to process (rules and regs about spinal matter.) But that's usually not until around 12 months old, often later. However, again if they are for your own consumption, they may develop more flavour in their second year and in truth it doesn't cost that much more to slaughter hoggs with adult teeth - our abattoir charges an extra couple of quid is all.
If you can get to ScotSheep next week, visit the Eblex stand - they'll have lambs and models, diagrams and experts to help you understand all that.