Where do I start?
What resources are useful?
Use this forum's search feature to look up the dozens of threads already here about learning PHP.
Is it better to write php from scratch or use existing open source code?
It all depends on what you need to do, what your skill level is, what your schedule is, and what your budget is.
How does phpMyadmin work?
Quite well, thank you. (And see next answer)
How does MySql and phpMyadmin relate?
MySQL is one of many relational database systems that can be used with PHP. phpMyAdmin is a PHP-base web application that allows you do do many database admin and general usage tasks via a web page interface. (If you opt to use PostgreSQL instead of MySQL -- as we do where I work -- there is a very similar app called, appropriately, phpPgAdmin.)
Teach yourself: that's what most of us did. :p :o