I'm not sure if this is the right place to post, but in lieu of creating a new thread I shall put to you this question:
This would be better in PS3 General Discussion, but mainly because the game saves aren't your issue.
https://www.gtplanet.net/forum/showthread.php?t=63832&page=647
I'll explain.
My PS3 is a mere 40gb and I expect a few more PS3 games on the way these holidays and there is no way I will have room to accompany existing saves and those the new games will require (and I do NOT want to delete existing saves). Short of upgrading my HDD or getting a new PS3, am I able to:
Game saves are only taking up, at most, a few megabytes per file. Most are only Kilobytes in size. Your focus on game saves is misplaced.
What you need to worry about is Game Data files. These can be up to 5GB in size off of a plain install and much larger with DLC add-ons (My Rock Band file is 13GB). For games without DLC add-ons you can delete those without losing your save file. They are under different menus in the Game section of the XMB. You can delete Game Data with DLC, but you will have to redownload all of that at a later date to get it back, so I would save those for desperate times. With non DLC games you only need to go through the game installation process and any updates again.
PSN games can also have game data deleted without affecting saves, but you will have to redownload it to play it again.
In short, the best way to free up space is to just delete game data. Your game saves will remain untouched unless you delete them and barely take up enough space to be an issue.
a) Run games off the existing saves on to an external HDD (assuming I've transferred the save files from the PS3 to the external HDD and deleted them off the PS3 beforehand)? Or can I only run saves that have been uploaded onto the PS3 before playing the game?
You cannot run game saves or game data off of an external device. It must be on the internal HDD. So, you would have to copy the files back and forth, assuming the game data or game save will allow you to copy it off.
b) Will uploading saves from an external device such as a HDD void my ability to earn trophies/disable other features?
If it is your save that matches your system then it shouldn't make a difference. However, some games lock the save file, some won't let you earn trophies if the save file isn't originally linked to your system, and some won't let you earn trophies that are on the save file but will let you earn them if you do the act to earn them.