Why won't my pictures transfer from my old iphone?

I got an iPhone 5s yesterday and I've been waiting for my pictures to transfer over all day and night. When I go to camera roll it says that there are the amount of pictures that I had on my old iphone ( a 4) but when I go into camera roll they're all just a bunch of gray squares and at the bottom it says downloading. Anyone know how to fix this? Btw I would rather not plug it into my compute because it's not a Mac and sometimes it screws up stuff, so if I could do this just on my phone that'd be great

Why is my iphone battery jumping levels?

I had it at 60% last night and decided to charge it overnight! Then it went to 6% this morning! With the charger still plugged in!
What
s more, It just turned itself off and I plugged out then in and got 10%
Now it's a measly 2%! WHY?!

IPhone charger/connector plug not working with macbook air?

IPhone charger/connector plug not working with macbook air?

Added (1). I can connect it to the computer, but my phone just vibrates on and off continuously, which means it's disconnecting and connecting every half-second. It's a refurbished macbook that I just bought a few weeks ago. Cord works fine on my other computer (a Dell) and works fine when plugged into the wall.
I do have Applecare, should I call them?

Icloud experts need your

So I deleted my icloud account on my iPhone for personal reasons, and now all my contact have no names I see numbers but without names. Is there any possible ways I can get them back?

Bought an IPhone can't download apps?

I bought an iPhone from someone online. It's fine except I can't download any apps because it keeps asking me for their apple Id and password before I can download which of course I don't have. Is their anyway I can change this account with my own details? Or am I stuck?