And how do the horses age here? Is there a fixed rule or do they just age as we are playing with them?
Just briefly adding my bit- there's no fixed rule. There's a suggested rule, which Allison has kindly listed, but aging of horses (or their riders!) is not enforced... some of us don't age our horses at all. The only instance where this might possibly be different is if you plan on competing in flat racing/steeplechase? I'm not 100% sure whether that has changed.
If you're still having problems with the 'website' field on the stable creation page, you can just write 'http://' or 'nil.' It doesn't have to link to an actual webpage.