iPad help

I have a few questions about our iPad. Is there a way to permanently delete an app? Like if the app is in the "purchased apps" but doesn't get used. We've downloaded quite a few apps because my son is super picky and only likes certain ones. So we would download them and give it a test run to see if he liked it. But now I find us with tons of unused apps.
Also, it seems to be running slow (got it in late September). I double click the home button and close the apps that aren't being used. But it doesn't seem to help much. I'm wondering if it has to do with the amount of storage we have left. I don't have any songs on iTunes downloaded. Just one movie. Maybe the movie is doing it? Idk