Great question. SQL is the standard language for talking to relational databases (RDBMS). MySQL is a particular implementation of an RDMBS, along with PostgresSQL, Oracle, IBM's DB2, and others. You can use SQL to talk to any of those (though there are non-standard vendor extensions).
That's an important part of the reading for today. I just went over it, but I'm happy to address followup questions.
Yes. There's even a client for node.js. See npm node.js mysql. Nearly a million downloads this week!
Data representations that make joins efficient, mostly hashtables and B-trees. B-trees are super cool: Basically a tree with a branching factor determined by the size of a disk block, which could be in the hundreds. O(Log200 N) is very fast.
Inner joins are when we only want matches. Think marriages or couples dance partners. Left joins and right joins include the single folks.
Because the batch files begin with a use other_db;
statement, which changes the database. But the other way just suppresses that message.