Nice questions. I am aslo interested in these problems.
In my opinion, DApps are the same Apps. But Apps have to run in the host servers, if servers are shutdown then Apps die. DApps will run forever if it is still used by users. So, I think your problems about DApps will also solved as same as they work in App.
By the way, I have a question too. Is there DApp store, likes Google Play or Apple's App store?
If with Dapp Store you mean just a place where you can do the DApp discovery and use them as well , yes, you can do that with some wallets.
For ETH DApps i only am aware of Parity UI and Vault.io.
They both have DApp discovery and interaction.
But i still haven't figure out how those wallets rank the DApps in the directory.
Especially when the user does a keyword /tag based search , or he simply is browsing by category.
Probably the ranking algorithm is specific to the wallet, so we should directly ask the Parity or Vault.io team.
Another thing... from the Parity wiki I've read that you have to spend 1 ETH just to publish your DApp!! That's crazy.
Check this
https://wiki.parity.io/Register-your-DAPP-for-discovery