In talking to people both familiar and complete strangers to Ethereum clients, these questions were asked more than once.
Soon. We’ve got some network simulations and a public testnet already running for Ethereum 2.0, and we’re syncing up to block 1.5 million on Ethereum 1.0. To stay in the loop, please follow our development updates on our blog.
With light nodes, they ask “give me the data to check if this transaction has been confirmed” and then check on their own. This is a trust-minimized setup which combines the best of both worlds - very little storage and processing power required while allowing for cryptographic verification of the full node’s claims.