DanielB,
Yes, there is a fairly large calendar of events and besides the listing on the SAF website the Scottish Hill Runners Association produce a comprehensive calendar that lists Highland Games races, bike/run races, etc. It's usually out in February and gets sent to you if you're a member, alternatively it can sometimes be found in Tiso's.
Hill Races are graded short, medium and long according to the winning time and A, B, or C according to steepness so races may be listed AS, BM, CS, etc. I'd stick with the short races at first to get a taster: 10km could be a pretty tough race and distance is not as relevant as time. A midweek evening race would be a good place to start
Plus points for hill racing are that it is much easier on the joints: no hard tarmac to contend with. I can't think of any downsides!