File node.tpl.php: Is there a way to edit without modifying the core file?

All themes contain a node.tpl.php file which can be edited. It is also easy to make a customized copy of any theme (by renaming it and editing its .info file), which you can place under sites/all/themes, and use that one instead of the original.

In any case, also check these modules:
http://drupal.org/project/weight
http://drupal.org/node/398508

you could use a views block

You can create a sub theme. Or try http://drupal.org/project/custompage though i haven't used it so not sure if it'll fit your needs.

http://drupal.org/project/contemplate might also be useful.

Thanks for your replies.

I'm still in newbie status so even though I might not quite know how to apply some of your replies, the more I continue to use this software, I'll get there.

@cog.rusty - I checked out your references and for 'Comparison of Node Ordering Modules', although I couldn't see the entire table (sidebar overlaps last column), it looks like very important info as to the understanding the infrastructure. Good stuff.

@lasac - I wish I knew more (something) about views. That's on my to do list. Hopefully I can find a good tutorial on it. If I knew more about it, I could figure out how to order the sticky nodes which I still haven't figured out and haven't gotten a response to a previous thread I created, so I'll be winging it. I'll write some kind of routine in the node.tpl.php file now that cog.rusty explained how I can make changes.

@duvien - I'm going to look into your suggestion of a sub-theme as soon as I get past coming up with a way to order front page stickys the brut-force way (I'm not going to alter timestamps) and hopefully get a solution to my feeds not updating dilemma that I posted earlier today.

I got my hands full.

Thanks again folks!