Deleting redundant files on remote server

Complete novice here, so bear with me...

I've found myself in the unenviable position of being the most tech-savvy person in a small non-profit.  as such, the responsibility of updating/managing the website has fallen to me.  That this has fallen to me is a woeful indictment on our ability to find and keep competent tech people, but it's the situation we have, so...

Best I can tell, the remote server seems to have several similar folders containing various iterations of the site, none of which are complete...but which, collectively, seem to function reasonably well.  For the most part, the site has been cobbled together in php, with a smattering of html sections.  Again, this is what I inherited and I'm only about 80% sure I even understand what's happening.

The trouble I'm having is when I try to make edits to the content, I can't easily find the files related to specifc pages without having to open every folder and open a half dozen not-quite-right versions of the page I need, all of which (of course) have the exact same name as the file I need.  As an example, there may be 8 files called index.php  If I can find the right one, then I have to try to trace back the links to properly place images, docs, etc.  Seems very tedious, and I have a hard time believing that this is the best way to make changes.

What I'm look for is a way to seek out the most up-to-date version of each page within the remote server folders, and delete the others, so I can pare down the contents of the remote server folder—ultimately making it easier to pass this project off to someone else.  Of course, I have significant concerns about making a mistake and taking the site off line, so I haven't gotten too agressive yet.

Where should I start?  Is there even a way to search for files in DW?