Do I understand this correctly: With PepeCash I can buy PepeShares which are basically trading cards. The shares can fall or rise. Also the shares can be burned and I'm loosing everything. Is this right?
Nope.
Check
http://rarepepedirectory.com those are all the cards currently available on the Counterparty Decentralized Exchange (DEX, which runs on the Bitcoin blockchain). Those can be bought on the DEX using XCP (counterparty's native currency, which is just an asset inside the Bitcoin blockchain) or Pepecash (which is itself a card too).
The shares are from the game, and they are called RAREPEPEPRTY (that's the Counterparty asset name of the shares). Those shares represent participation into the game's earnings. The business proposal is at
http://rarepepe.party with earnings explanation, etc.
The rest of the cards are just assets inside the Counterparty system that can be bought, sold and exchanged freely on the DEX (again, all this happening inside the bitcoin blockchain). The game will let you use those assets on your addresses inside it, playing as MtG, Heartstone, Pokemon or YuGiOh cards.