Hi - my knowledge of databases is very fuzzy. I am plannig on learning it soon. Am I right in thinking that you only need ONE installation of a MySQL per computer....and this could then be used by different platforms? For example both PHP and RubyonRails could both run of the same installation?
Yes, you are right. All clients access the mysql database over the network, thus there is no limitation on the clients (programming-)language. See the mysql downloads http://dev.mysql.com/downloads/ for some client connectors from mysql itself (there are more).
Yes, you are correct.
Mysql works with server (installation) and clients. Normally the server only accepts clients that run on the same machine. Meaning you can have many clients running from the same database server which holds multiple database.
It is also possible to allow mysql to accept requests from clients from other computers. Then you would only need 1 server for clients on many computers. Do note that you have to think about safety and firewalls when you allow mysql to accept remote connections.