Does Elastos have a wallet?
Yes, 3 actually: Elastos Wallet, Elephant Wallet, Web Wallet.
FIXME: Page not found (discover_elastos/core_modules/wallets.md for “More about wallets.“
Can I store my ELA on my Ledger Nano?
Not yet but Elastos integration is in their roadmap. This should be available by Q4 2019.
When will there be an official wallet app for my smartphone?
The Elastos wallet already runs on Android and iOS.