Problems with my iphone apps?

So last night i had tried to jaibrake my phone and it had crashed. I backuped everything and everything still got erased besides my contacts and pictures. I had bought multiple apps before the crash, when i restored my phone i was able to get everything i had installed back including all bought apps EXCEPT my music download pro app that i had bought! How can i get it back?

Why does my iPhone 4 battery go down so fast?

I'll use it for Internet for like 10 minutes and my battery will go down a percentage every 1-2 minutes I hate it. If I take it to the sprint store will they help me? Or will I have to take it to an apple store? Or can you guys give me tips on how to save battery?

How to bypass IOS 6.1 activation screen?

I accidentally upgraded to 6.1 like an idiot yesterday due to the new jailbreak. But forgot that I had to bypass the activation screen. When running 5.1.1 i was able to do it with a method that worked, now that I'm stuck I do not know what to do. The new jailbreak will not allow me to even jailbreak my device. I don't use it for a phone its an ipod pretty much(IPhone 4) Can someone help provide an answer or even try to help in how to downgrade back to 5.1.1. I was not using any sort of sim card when it was running 5.1.1.

How to download pictures from my Mac Mini to my iPhone 5?

All of the answers I've found on here say to use iTunes, but there's no tab in my iTunes for photos. Even when I go to Preferences>General and look at the Show: it has check boxes for all of the things I want it to show, but it doesn't include Photos. I've tried to drag and drop photos in iPhoto to my iPhone, but it won't let me do that either.

Why won't my iPhone 5 charge?

I had my phone charging all night and when I woke up it was at 35%. Sometimes it will charge and sometimes it won't. A little over a week ago it kept turning off on me.

Is there anything I can to do try and fix it?
Is this a common iPhone 5 problem?
Should I take it to Verizon or Apple?

Lost my iPhone, can I track it?

Is there any way to track it? It's an iPhone5 and I tried calling back from a different phone number it rings once and then it was going straight to voicemail. After hrs of calling and the same thing happening I called and now it goes straight to voicemail. I'm not sure if I misplaced it at home or I simply lost it running errands.