Edit modules/comment/comment.tpl?

I am looking to make some changes to the commenting system on my drupal page. Stuff like getting rid of the "X new comments" notification, changing "add a new comment" to "0 comments", etc.

However, I am using the Tapestry theme which does not have a comment.tpl file in the theme folder. So, should I just modify the comment.tpl file in the modules/comment folder, or will all those changes be overriden if I install an update for Drupal?

Should I just create a comment.tpl file in my themes folder? If so, how do I point my theme to use that file or will it just do it automatically? Also, I'm unsure how, if I'm just ADDING an additional file, I would make it GET RID of the things that I want to get rid of (like the "x new comments" notification).