I had a 3 season room in the back of my newly purchased home that has these types of screens in them. Unfortunately a lot of them are broken/need replaced but I don't know why type of screen this is (w/ this spring loaded tab at the bottom). What are these and can I use an alternative?
As mentioned in the comments to the question, most window manufacturers have custom window screens that fit into specific window profiles (though, at times, you can come across very similar or identical profiles, depending on whether or not a manufacturer shares a supplier with a competitor).
For the screens that you have with damaged mesh, you can replace/repair those by procuring new mesh and new splines*. To remove the screens without cutting them out you typically just have to pry or pull out the splines from the narrow grooves in the screen bars (as those splines are what holds the mesh into place) which will allow you to remove the mesh in one piece. To install the new mesh, drape it over the screen frame, allowing for excess material to hang over the sides. With new splines, use a narrow/dull tool to press the spline+mesh into the groove in the screen bars, making sure the mesh is taught. Once in place, trim the excess spline and mesh material. There may be a warp in the screen framing from the way the tight mesh pulls at it but that is normal (that warp typically goes away once on the window).
In the case of the damaged spring locks that hold the screen into place (or missing screens in general), you will likely need to go to a window supplier/manufacturer to replace or repair the screen. However, if the window is too old or you are unsure of who made the window, you may need to find a substitute instead. Finding a substitute may require you to visit and consult with a couple sellers/manufacturers about using their products in place of your damaged screens. Though, keep in mind, replacements may not necessarily fit well but it will at least do the job.
You will likely be directed to the Service department for this and I would recommend taking with you at least one of your screens for reference along with clear pictures that show what the window profile looks like. Those pictures are needed to give a Service tech a better idea of where and how the screens are mounted. (Note: window manufacturers will require specific measurements before ordering replacement screens. Depending on the company, those measurements may be taken by you or a Service tech on site. I recommend waiting for feedback from a Service tech whether his screens will fit in your window first before taking measurements. He/she should tell you what part of the window to measure).
*Metallic wire or rubber lines that are typically pressed into narrow grooves in the screen bars. The splines are what hold the mesh into place.