Mobile internet not working on new sim?

So, I have just got a new sim and I can make calls and send texts but for some reason, I can't go on the internet. Wi-Fi works fine but the mobile internet is not working. I have just got an iPhone 4 and from what i can see in the settings, it looks to be alright. I have 500mb of data included in my pay monthly SIM so there are no other reasons for it to not be working.
Any help would be muchly appreciated!

How long does the apple store take to deliver? UK?

How long does the apple store take to deliver, i want to order an iphone 5 but it says delivered in 3-4 weeks, but thats a long time to wait with no phone because i will have to cancel my cirrent pay monthly sim, but is it really 3-4 weeks? Or is that a safe estimate?

IPhone contacts got deleted?

I bought a new iPhone and before i plugged it into my computer to restore it from my last backup, i added new contacts. Once i got around to restoring it from my last backup, it lost all my new contacts, and any communication i had with them (i.e texts, calls, etc.)
Is there any way to retrieve these contacts?

Why iphone isn't sending video?

My girlfriend send me a video from her Iphone and when I received it it popped up as a GIF image moving slowly. Then I told her to send it to my gmail and yahoo email account because usually if for some reason a video doesn't send to my phone I can always rely on my email accounts to receive it and then I'll just download the video from there easily without any problems. Nevertheless, I received the video but in the same GIF image format. Why does it send the video as a gif image instead of a real time normal moving video. Is it her settings. Can someone let me know how to correct this problem so I can explain to her how to fix it?