I tried to post a screenshot of my email program and that's when I got the message that it was too large. yes, it had to do with the limit on the forum.
Not much you can do about that, the TS forums have a limit of ~1000KB total bytes, 500KB per image. The point is, that has nothing to do with "memory problems" on your Mac.
However, instead of making screenshots via the Mac, you can use any number of other apps that can usually make them as jpg's. The second image below is from a Mac "Screenshot". Its size is 1.04MB. The image I posted is from running that png thru Photoshop
Elements and converting it to a 60% "quality" jpeg, reducing it to 32.4 KB. Mac/Apple screenshots can be massive, that's just a function of png's. While they are waiting to take up all that space on your drive, they are already trying to use your RAM.
If your Mac is using 7.12 GB out of its 8 GB installed, it is no wonder that you are having apps quit or there are memory warnings.
Take a look at Activity Monitor, again. Click the "Memory" tab. Now click the "Memory" column until it lists items from high to low. What are the top 5 items and their memory usages? You can also see that there are hundreds of things (mostly OS related) that take up your available memory. Since you didn't post an image of what AM was showing, we can't offer more detailed help.
Last suggestion; reduce that number of apps you have open all the time.