Go into your email app settings and change over what time period you want to see emails for. For example, you may only want it to download emails from the last three months, one month, or week(s). If you are using something like a GMail account or similar, then your older emails will still be available via the website. Also, you can change a setting telling your email app not to automatically download attachments. As for Facebook, I find the website easier to edit than the app. So, delete what you don’t want from there and your app should synchronise with that.