I accidentally deleted the Yosemite's Photos App from my Applications folder but I can't seem to find a separate download link anywhere.
It can't possibly be that I have to re-install Yosemite just to get the app, can it?
MacOS – Separate download of Photos App for Yosemite
macosphotos.app
Related Solutions
With the plain screen, click on "Go." Under it, you should see the "Home" folder. If you click on it, you should find all your folders. I have tagged them a certain color so I can easily find them.
Hope this helps! 
As Photos is supposed to be included in the 10.10.3 update automatically, I would suspect something may have gone wrong with the OS update itself.
In cases like this, I would always try downloading the current combo updater from Apple - currently 10.10.3 from https://support.apple.com/kb/DL1804 but you can always Google for "Apple combo updater [current number]" to find the latest.
The combo updater, unlike the regular delta updater, includes all changes since the last major update, in this case 10.10.0
I would also run Disk Utility & check permissions & drive integrity - before & after running the combo, just to be certain.
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Best Answer
If you use Time Machine, just restore the app (and its data, if applicable) from an older backup. If not, reinstalling OS X is probably the best idea, as Photos is not available on the Mac App Store and I definitely wouldn't try to download it elsewhere (so don't just type "Mac Photos.app installer" in Bing or Yahoo or Dutch and download whatever comes up). You could copy the app over from a friend or family member, though, if you wish.