1. no, you'd run the MySQL server from the command line (or have it start up automatically)

2. it's a database. it allows the computerized storage and retrieval of information.

3. i don't know what "glom" is, so i cannot compare/contrast the two

4. yes, you'll need an account to log in. both server and client can reside on the same machine, or on different machines.

It sounds like you were looking for some sort of application to do your 'business tasks' with -- think of a database as an 'engine' in a car: with just an engine, you cannot drive anywhere - you need the rest of the car (the application). Then, you may need tools (knowledge of programming, SQL, etc.) to either build the car (application) or to keep it tuned up.

A database, by itself, will not do anything except take up some space on your computer. It sounds like you probably want some sort of business application that uses MySQL (or any of several alternative) databases for storage/retrieval... and specifying, designing, building, debugging (and so on) of a database application is well beyond the scope of this forum.