Setting up MythTv can be difficult, but it's also a good learning experience. I finally got MythTv set up a few days ago. I still have to figure out a few more things, but at least I can watch TV and listen to music etc. The documentation on how to use MythTv is not the greatest so it's taking a little longer than I wanted.
The instructions on how to install it is pretty decent though, as long as you have all the pre requisites.
...anyway, to answer your questions.
You don't need a partition of the database. Make sure you have MySQL installed and that the database is running.
'mythtv' should be a user. The user is normally created before you install MythTv, but I am not sure if it's required.
When they say 'cd database', they mean that should should change directory to the 'database' directory (after the downloaded file as been extracted). The documentation
This is the mc.sql script, and all it does is creating the database and give access. I am not sure where the actual database populated, but it's probably in the setup somewhere. Did you run the mythtv-setup? If you didin't have the database at the time, you will have some problems.
CREATE DATABASE mythconverg;
GRANT ALL ON mythconverg.* TO mythtv@localhost IDENTIFIED BY "mythtv";
FLUSH PRIVILEGES;
GRANT CREATE TEMPORARY TABLES ON mythconverg.* TO mythtv@localhost IDENTIFIED BY "mythtv";
FLUSH PRIVILEGES;
mysql_install_db that you mention is not mentioned in step 6 of the documentation:
http://www.mythtv.org/docs/mythtv-HOWTO-6.html
I am sure you can run this manually, but I did not run this manually myself, so it was probably ran during setup.
Your access problems is related to the fact that mythtv needs a mythtv user/account (also see database script above), so you need to create a mythtv. I also had to change ownership of a couple of files later.
I hope this helps a little.