Your first question is answered above, but your second and third I will address.
No, you don't need to unless the app is failing in some way and you actually need the app to fully restart.
Killing an app does NOT make the iPhone charge faster. Anyone that tells you otherwise came from Android or read too many Android forums. The only thing that can slow an iPhone down while charging is actually using it.
Trick question. Open has many interpretations. For example:
Launch Music app and start playing music. Hit the standby/lock button on the top of the phone. Is it open?
Launch Mail app and check mail. Double click home button. Kill Mail app. Is it open?
The answer to both of those question is YES. So if you are taking about apps that respond to real time events like GPS, Music, SMS/MMS or notifications they ALWAYS have a section of code open and running. But games, web browsers, news apps, camera apps and the like, they are in memory but don't run any code until you are actually interacting with them. So leaving them loaded/open does not drain anymore battery than having them not loaded/open.