Can you see what I searched?

So I have an iPhone 4S and my mom pays my bills. So I don't use my data but if I do the will it show on the bill? And will it show what I googled and everything I did while using my data? Majority of the time I use my Wi-Fi. So I go on google, twitter, etc and I'm wondering if It will show on the bill? I'm scared that it will show what I've been googling because I go on po*n and I don't want me mom too see. So can It show at all? Anything? Like twitter app, google, etc?

What is the fastest DNS server?

I have an iPhone 4 that buffers YouTube videos constantly and I heard that if you change the DNS on the phone the buffering will speed up. What's the fastest open DNS out there?

IPhone randomly disconnects from Wi-Fi?

It's a 3gs that I've had for a couple of years and it doesn't happen that often, but it just does it randomly disconnects from Wi-Fi while I'm using it. I'll be messaging someone on Facebook and all of a sudden a notification pops up saying something about Couldn't connect to internet. I go to the Wi-Fi on the settings and there's no available networks to connect to, not my network or my neighbors'. I turn off the Wi-Fi option, I reset my phone, I reset the modem, I manually enter my network information on the 'Other' option, everything and it stays the same. My brother also has an old 3gs, but it never happens to his.
I just wanna know why this happens and how to fix it because it's freaking annoying.especially when I'm in the middle of something.

Added (1). I also reset the router*

How to allow apps access to my photos?

I recently updated my iPhone 4S and now I can't for example upload photos to Instagram.

I've gone to settings - privacy - photos but there's nothing there! It just says "apps that have requested access to your photos will appear here".

I've tried everything, please help!

Why won't my iTunes let me sync music?

Okay so I'm trying to put some songs on my iPhone 3GS. I made a playlist, selected it in the bit where you check what you want on the device, clicked sync and then checked my phone. Nothing is on here, except existing music.
I thought maybe I had too much stuff so I deleted my old music (un-ticked it all) then synced it again. All music deleted.Re-checked this new playlist. Synced. Still nothing on my device.
Then I thought, maybe it's the playlist? So I individually selected each artist. Synced. NOTHING.
This process lasted well over an hour. I'm not computer savvy, certainly not iTunes savvy, so could someone please help me? I need this music for my Christmas break!

My iPhone 4S call speaker doesn't work?

When I talk on the phone, I don't hear a ring or the other person on the line. My sister said she can hear me talking but I can't hear her. I put it on speaker and it worked.