As far as the RAM (memory) is concerned, my understanding is that any apps you run will take up RAM, and simply exiting will not free it up. The OS keeps it in memory (but usually not running any processes, unless it's one of the few apps that are permitted to run certain processes in the background (Skype, etc.)) so the next time you launch it, the app launches faster. If other apps need the RAM, the OS will free up that RAM. (Essentially, if it cannot be used for another process, might as well have it hold recently used apps.) All this is supposed to be transparent to the user (in theory). You can manually "end task" these apps to free up some memory if you open up the task manager, and remove them from the list. It will not free everything. Memory management is supposed to be handled by the OS and not require user interaction (again, in theory). It generally works well as most apps are not permitted to run in the background and are sandboxed.
If you frequently run into issues with crashing apps, etc., then the best course of action is to wipe the device, set up as new, and reload everything from scratch. This process will delete all data including text/iMessage messages, game history in games (have to start Angry Birds from the beginning), and anything stored locally by apps. Generally, I always do this with each major OS update, but I admit it is a pain in the neck to get everything loaded back in (and losing text messages, etc., is kind of a bummer). Restoring from a backup could just restore whatever data/configuration/etc. that is causing your issue. But if you do perform a wipe/setup as new/reload, you will essentially be setting up your phone as if you just got your first new iPhone with nothing on it. All data will be gone. If that does not fix various apps crashes, you either have to find the offending app or make an appointment with Apple.
As far as the storage goes, I've been told the "other" can be stored data from any number of apps (I think Safari cache, etc., are included in there). The only way I've been able to get this number down is to do the wipe/setup as new/reload procedure (and as I start using my apps, it fills up anyway).