Frequently occasions, after i consider adding my very own custom PHP source codes towards the template files (sidebar.php, index.php, header.php, etc...), it creates errors. However, it really works correctly by itself outdoors of Wordpress. It is possible to way that i can use my custom PHP stuff in Wordpress' template files?

If you are speaking concerning the sidebar.php, index.php and header.php in wp-content/themes/themename/, well, obviously you can edit these files. They're intended to be edited. Only make certain you don't overwrite existing PHP functions...

Read about this on Wordpress' Docs

No wordpress plugin needed to include your personal php, but to keep upgradability you need to, so far as possible, avoid changing core Wordpress files and put your code in your own theme's files or in your plug ins. If you are getting errors it's difficult to guess at the things they might be without particulars, but I have discovered that, aside from simple parse errors etc., probably the most likely causes are scoping errors.

With Wordpress you are able to extend Wordpress functionality by writing your personal plug ins. This can be a fairly discomfort free process.

http://codex.wordpress.org/Writing_a_Plugin

You may also extend the functionality that templates have by putting functions in to the functions.php template file.

http://codex.wordpress.org/Theme_Development#Theme_Functions_File

Adding custom php code to templates should not generate errors. The only issue you may be getting is your code is conflicting with existing wordpress function names and variables.