When I open some applications, they force quit immediately

This usually happens when the applications are not supported on your system. Try searching around for older versions.

How much RAM do you have installed and are you running the OS version in your profile (since you posted under Snow Leopard, but show Lion). And, how much empty hard drive space do you have? All the apps you mentioned except for Skype do need plenty of RAM and plenty of hard drive space to function properly.

You need to maintain an absolute minimum of 10 - 15 GB of hard drive space at all times for the OS to run properly. Now, FCP is another matter - editing, rendering, etc. need a lot of hard drive space and the general rule is: you should have as much empty space as your files in your current project. When I do a one hour HD project, I can easily amass 100 GB of temp files, so that means you should have at least that much empty space. So, you can't just delete 5 GB and think that's ok - you need to keep moving your space hogging files to another drive and/or let FCP, iMovie, etc. access their files on an external hard drive. You can move your libraries and set up FCP to use an external disk. Here is how to move your iMovie library:

http://support.apple.com/kb/PH2302

For FCP, try Preferences and/or System Settings (that is where I set the scratch disk in my older Final Cut Express) and it offers options to set a different (external) disk:

The quickest would be by moving all your space hogging files to an external drive and then deleting them on your hard drive. Deleting applications doesn't do much and you shouldn't delete any applications installed as part of the system. You can delete third party apps or files in your User folder.

I do not know why Skype does not open or crashes - do you have the appropriate version compatible with your OS version? A reinstall of the OS might be in order, but we need to know exactly which OS version you are running.

How much RAM do you have installed? 4 GB won't do it for FCP - I'd consider a minimum of 8, more is better.

There is some corruption somewhere. I believe it is time for a reinstall.

FWIW, do you have any AV or socalled "cleaning" software installed?

You still have not said which OS version you are running.

And, check your Activity Monitor to see how much RAM you/the apps are using.

No, no, you don't want any cleaning software - I thought you installed some maybe and it was causing problems.

Thanks for the screenshots - you left out the one for System memory - I'd like to take a look at that.

You can also disable Software Update so it does not run continuously - but then you would have to check for updates manually of course.

Well, although I consider 4 GB RAM an absolute minimum for any OS Lion and later, the screenshot does not indicate any RAM shortage (at least when that was taken) - absolutely no swapping going on.

If you continue to have the problem, I'd really consider erasing/reinstalling (try to install your apps from scratch). And/or delete the apps you have a problem with and re-download/reinstall them from scratch.