Some post-related questions.

I want to be able to post on more than one page,like this wordpress site. They have posts on more pages(Tutoriale,Free Stuff..)
I think I found both solutions to this problem,but i need some little help.
1)Someone told me to post posts under categories,then click on that category and all posts wich were posted under that category will be displayed there. But there are some questions I’d like to ask.
Can I rename that title(Category archive: <name>)?
Do these category-archive-pages work as normal pages in the menu?I mean,can I put them in the main menu,near Home?(I tought about creating an item that links to “that” category-page)
2)Someone else told me to edit the source and add some php code which makes a certain page display all the posts from a certain category.
How can I edit my site’s files?Is this correct: Download/install wordpress,edit files(write code),upload via FTP client.
He told me to modify page.php this way:

[Code moderated as per the Forum Rules. Please use the pastebin]

but again I have some questions:
How should I add the code?Should I replace everything from page.php with this or should I just add it like it is?
Every theme has its unique page.php file?Because I found it more than once in /wp-content/themes/twentyten and /wp-content/themes/twentyeleven .
How can I upload these files using FileZilla?

And finally ,the last question: Which solution is the best and which one should I use?
PS:I know I asked many “dumb” questions but I’m a beginner and I’m completely lost.Codex is so big and gives so many details!
Thank you for reading!If you don’t understand something,ask me!