It’s safe to store a small stack of photographs together. It gets tricky when they are different sizes, since that can cause bending, plus a corner of a smaller photo can nick the emulsion of the one next to it. But same size prints in an enclosure that keeps them snug is OK, since they won’t be able to “knock about” even a little bit.
Here are two specific bits of advice for your current set up:
(1) Don’t write information with pen on the back of a photo. That’s always true because it breaks the Golden Rule of Preservation which is “don’t do anything you can’t UN-do”– but in this case it’s also because you’re going to store the prints stacked together. You don’t want ink from the back of one to transfer to the front of another. Use a Stabilo All pencil which is eraseable but will write on a plastic-y photo print.
(2) The bigger risk here is the UV light it’s getting from sunlight and/or compact florescent bulbs. You can swap out the frame glass for plexiglass that has UV resistance built right into it, or cover it with a UV protective sheet that’s sticky on the back. If you choose the former, I think any decent frame shop that does museum-quality work should be able to sell you that. In any case, each photo is only on display for 1 year so this is less critical than it would be with a single photo.
Photos taken by other people are an odd category and often get overlooked and lost in the shuffle. Recently, I’ve decided that for the digital versions (emailed photos, shots you download from Facebook, etc) my best advice is to create a KEEPER folder for them all. Strength in numbers and all that. One for each year or month/year depending on how many of this kind of photo you have.