Hello again, Pinkcowprint.
As I indicated above, I've flown with Ryanair quite a lot and (even though I only ever have light cabin baggage myself) I try to take note of what they actually do regarding cabin baggage.
The first thing to stress is that, at many (but not all) airports, they're very strict about the 'one bag only rule'. That means that things like handbags and airport purchases all have to be squeezed into a single bag. (If a passenger tries to board with an extra bag they'll simply meet with a refusal at some airports or a �30/�30 fee at others).
I've only rarely seen passengers required to put their bag into the 'measuring cage', but it does happen (usually when the bag is blatantly too big). To be fair to Ryanair, airline safety rules require that any large items of baggage have to be stored in the overhead lockers. Since the loading limit for a single locker (which has to take several people's bags) on a Boeing 737-800 is 56kg, it's understandable that a 10kg limit is imposed for each passenger. It's also reasonable that bags have to actually fit into the lockers. (The lockers on 737-800s aren't particularly big. If you do manage to sneak an oversize bag into the cabin, it might not fit into the locker. The safety rules would then require Ryanair's staff to refuse to carry that bag within the cabin).
Whickerman's post suggests that you need to check Ryanair's policy on buggies. I'll save you the trouble of looking for it. See here:
http://www.ryanair.com/site/EN/faqs.php?sect=b ag&quest=infantequipment
and here:
http://www.ryanair.com/site/EN/faqs.php?sect=b ag&quest=cabinbaggageallowance
Chris