You can uncheck "Automatically sync new apps" in iTunes. This will avoid the situation where iPhone apps that you don't want to use on your iPad wind up getting synced over. Other than that, the only current solution is to manually check off each app you want on each device.
iOS at its core now has its own multitasking API built in. The only way for an app to even go into the background it has to use these API's, so even poor programming experience still can't ruin things too much (and, with the flip side of that, poor developer experience could make the app while its running use more resources than needed).
All in all - this shouldn't be an issue. Those apps in the tray don't mean they are running - it literally is also a recently used app tray. And again, the background tasks they can do are limited by the backgrounding API, so like audio, VOIP, navigation, uploads, etc.
As far as being faster, have longer battery life, etc - no. At least not on an average. You may feel that it runs different, and yes there may be a rouge app doing something odd, and forcing it closed may help.
But in general, no - this shouldn't affect speed or battery life, unless those apps are currently doing background tasks such as location, audio, uploading files, etc. Otherwise, their RAM state is saved for quicker relaunch, but no processing power is being used.
Best Answer
Without the device being jailbroken or having a development provisioning profile installed, there's absolutely no difference between an app installed via the App Store or via "sideloading", except that one might be able to install an old version of an App Store app. Or possibly an app which the developer removed from the app store by choice. It's simply not possible to install any app that's not originally from the app store via "sideloading" without it being configured for development as all applications must have a valid App Store code signature. If you want to block installation of all apps, you can create a MDM profile with Apple Configurator with this restriction.