This, sir, are three questions. And I suspect all three might have been answered before.
As to 1: Answer questions all the time. That depends a lot on the distribution. Some of them ask a lot of questions and keep asking them whenever needed. Some, like Ubuntu desktop asked a single short set of instruction and then install in one go.
Whichever method you like depends on the goal. I hated when 'ubuntu-12.10-desktop-amd64' installed itself without asking me a lot of config questions since I had to undo some of the choices. If is very nice if you just want to test something without bothering the user, but for a server style install I want full control. And that means a lot of questions, preferably with sane defaults allowing you to press return a lot to use those defaults.
However there is no one single answer. All you can do is select the distribution which most closely matches your goals.
Is there any way to feed the installation a config file with all these settings (user name, locale, etc.?), so I can just press Enter, and then come back 15 minutes later to a completed installation?
There often is. How and if varies per distribution.
I want to exercise setting up a Unix machine, to make sure I can do it quickly.
If you want to repeatedly install a machine check of packages such as puppet. Configuring them the first time is a lot of work, but the next hundred servers are much quicker.
So I can install lots of packages and edit config files. But when I want to repeat the whole process from a fresh install, I have to go through the whole tedious installation process again (question 1). Is there a simple way to reset/backtrack Ubuntu to the fresh install I had? (ie. Uninstall all packages, revert all config files, etc.)
Note that I am not recommending this for a single server, or for two servers. But if you have many servers then configuration tools can save a lo of time.
Is there a tool that helps you automate setting up a Unix server?
There are many. A quick Google search on 'Linux automated setup'turned up
Those are just the ones showing up on my first search. I am sure there are quite a few more.