That's right OBE, yes.
It's split. Obviously there are performance and exposure related incentives, but for sales there would normally be royalties involved - usually 10% on the cost price - so if Nike sold a product in JJB that had cost £10 to make (and it had a Villa badge on), then Villa would get £1.
Depends where you buy it from, and also the %age royalty might be higher on shirts than other products. As above, if a shirt costs £10 to make (for simplicity of the sum!) and you buy it from JJB, then Villa will get a quid. If you buy it from the club shop then Villa get a quid, plus the retail mark up i.e. a retailer might buy it for £20 from Nike and sell it for £40, meaning you buy it from the club and Villa get £21 rather than JJB getting £20 and Villa £1.
Put simply, if you want more money going into the club, buy your products directly from them. It makes a MASSIVE difference.
Obviously there are other complexities in an agreement like this such as exclusivity on products, varying royalty percentages etc but this is a basic model based around the shirt only.