A full Blockstack core node can build up its local name database from scratch by iterating through the entire bitcoin blockchain from the beginning of history and selecting transactions that meet its rules and using those transactions to build the name database.
I don’t think so, but @jude or @aaron would have to verify.
Are you asking about full blockstack nodes versus nodes that aren’t full blockstack nodes? Currently the later ones (like we ship with the macOS app) are merely API endpoints that query and trust the configured for information about names. It trusts that the full node isn’t lying to it. It’s important to note that all nodes we ship have the code for to be full nodes, it is simply a matter of turning it on and waiting for the name database to be built.