Program Icons bounce, but won't open on Apple MacBook Pro

I just got an Apple MacBook Pro that is 5 years old and I have no idea how to use it or if something is wrong with it. I have 10.9.5 and it's supposed to be compatible and it didn't work. Since then, I've gotten 3 more programs from a total of 4 different places and they all do the same thing, so this isn't a problem just with one program or place. 2 of them had to be unzipped, then there was a rar file inside them that had to be extracted. The other 2 programs were marked7z; I unzipped them, then used the rar/zip extractor I got from the Apple store(i've used 4 different ones). Everything seems to work fine until I try to open the programs. I click or double-click on them, they say verifying, the bar fills, then the icon just bounces up and down on the desktop dock and the programs never open. I've uninstalled and erased everything, then downloaded them again and still same problem. They all just bounce, but never actually open. After waiting 5-10 minutes, I right-click and select force quit. I've inspected contents and everything looks fine; hash is correct; I can't figure out what's wrong. One of the programs has a .dmg and an .iso and when I click that them, they both say it isn't recognized. Am I doing something wrong with the extract/archive? I've never had an Apple before, but it seems like it should be easier than this to just download install and open a program.