Hat

Moulana Imraan Vawda has stated that it is sunnah to wear a hat.

1) Are there any specific conditions for a hat to be considered one that adheres to the sunnah?

2) If a male Muslim wears any of the following: woolly hat, pompom hat, baseball cap, snapback cap, bowler hat, fedora hat, fisherman cap, flat cap, fez hat or top hat; would the male Muslim meet the requirements of following the sunnah and would Allah reward him for this?