How to restore my apps on my iPhone?

.
I backed up my phone the other day and without asking me, the phone installed the new OS. My phone is the 4s It also deleted all of my apps that I have installed. How do I restore my apps they way they were?

I know, I should have gotten a better phone than the iPhone but I have what I have for now.

Is it possible to retrieve a deleted email?

On my iphone, while viewing an email on my gmail account, I must have accidentally hit the trash icon. Now even when I access my gmail on the computer, there seems to be no trace of the email even in the trash folder. Help?

Added (1). Wow, you were right Picklesberg, can't believe it.

How to stop my notes from appearing on other apple devices?

I have a lot of notes on my iphone. But then, when I use my mom's iphone, my notes appear on her notes app. Her notes also appear in my notes app. We use the same apple id so maybe that's the cause of this. Is there anyone who knows how to stop this? Also, I connected my iphone to itunes and i saw the "sync notes" is unchecked.

Why are photos taking up so much memory on my iPhone?

I have a 16gb iphone 5 and under usage it says 11.5gb used and 1.7gb available? First of all this doesn't make sense and i was just wondering why it says this.

also, my sister has a 16gb iphone 4 and has 3000 photos and it only takes up 5gb but i have 1500 and it takes up 7.1gb! Why is this? Neither of us have any videos either!

and. I deleted All of my messages but it still says messages takes up 1.5gb? Why is this!
i'm running out of space and whenever i take over 50 photos i need to delete another 50 because i keep running out of space!

Can you copy the Itunes application from one computer to another?

So I recently got an Iphone and I went to install itunes into my computer. The installation bar would reach the end but never let me continue - just the cancel bar would still be clickable.

I then noticed in the All programs (Windows 7) that it said "Apple software update" when clicking on it - it said "The Parameter is incorrect" so I can't progress further.

I've tried uninstalling itunes and redownloading. I don't know what to do. However my sister has itunes installed to her computer (Same make/model of pc) So I was wondering if I could copy over the application using USB? Or if not, how can I fix the parameter problem?

Do I have to update to iOS 7 on iphone 5?

Do I have to update to iOS 7 or can I keep the setting it has out of box and will all apps work cause I here's my battery during quick is cause of iOS 7 is that true or is it normal for battery to drain more wile on internet

Can I unblock a network blocked iPhone 4s?

I know it might not be moral/legal but is it possible to unblock an iphone 4s that has been blocked by a network?
I have heard about using a jailbreak to unlock the carrier setting, I know this works for a phone locked to a network for example you can jailbrake an o2 iphone to work with 3, but would this work for a network blocked handset?

thanks,

Added (1). I'm looking for the answer to whether or not it can technically be done.
Eg would the handset work if it was jailbroken although displaying 'no service' with a sim card installed in it.