Yeah, I think the wood and stone matches unlock doors in your castle that then allow you to purchase upgrades using XP gained.
Yup, although a number of the doors also have upgrades purchased via gold.
Here are the doors:
Top left: Sword/primary weapon upgrades - costs gold
Top right: Passive upgrades (time bonuses on certain matches, increased gold/XP, etc) - costs XP
Middle left: Armor upgrades - costs gold
Middle Center: Shield upgrades - costs gold
Middle right: Wand/magic weapon upgrades - costs gold
Bottom left: Potions (can activate individual potions that have pros and cons, unlock with further ranks)