It's more like Git where the latest action is linked to all previous action + data is organized in a tree so any piece can be efficiently demonstrated as a part of the trusted whole (via a merkle branch).

Yes; here's a tl;dr: for a given user, all of their signatures form a chain of signed statements, where each one points at the previous statement. They don't have to be the same kind of statement: your identity proofs, your tracker statements, etc.

And then each user's chain is itself pointed at in a leaf node of the signed merkle tree. (The tree is signed by Keybase).

So you as a client can verify any individual's personal signature chain, and you can verify Keybase's merkle tree. Finally, and this is the more subtle connection, each user's signature chain has statements about the merkle tree itself, so you can verify all these users are seeing the same Keybase-signed merkle tree.

A lot of the same techniques. No need for proof-of-work since there's no contention for a scarce resource.

We might, in the future, periodically write our root block to the Bitcoin blockchain as a further protection against forking attacks.