How to make my iphone stop asking for my friend's Apple ID?

Question

First question: why does apple website logs me out every minute saying "session time out" or something(i'm using chrome on iPad)..!
Second Question: why after i typed such a big question and when i switch tab and come back to this tab, the tex disappears (both chrome and safari for iPad)?
Before going to my actual question:
I(from USA) have an iPhone 5 and iPad 4, and bought the same for my dad(India), He has his own apple account and mine is separate.
I've recently send the iPhone 5 (factory unlocking it for 10$ before sending it to him- I have proof of purchase for all 4 devices)  after the 5s is released.
Third question: Why can't I add my dad's(Indian) phone number for iMessage?
Since I used that phone with my USA SIM card for 1 day before sending it to him, it remembered my phone number, but even after trying everything except complete reset on my dad's iPhone( since he can't manage to download all apps from scratch again) and didn't get a new sim yet, we tried everything but I couldn't make the Apple ID remember my dad's phone number..!
Fourth question: As my laptop broke, I used my friend's Mac to check the unlock is successful or not! Now when my dad tries to install an app from AppStore from his iPhone, it asks for password of my friend's Apple ID ,
My question is how to add his phone number and how to make it forget my friend's Apple ID
In Apple.com> manage Id> it doesn't show my friend's id anywhere. Do I need to de-authorize from his Mac?

Answer 1

Hi, I've tried a reset all, and restored from another backup(iCloud) and it stopped asking my friend's Apple ID(its been two days i've restored, and my didn't complain yet).
next, i've already tried all the steps you said.
my dad uses his gmail account for apple devices(same id for his iPad too), and i already checked "My Phone" number is set to my dad's phone number.
i asked my dad to turn off iMessage and Facetime, removed the sim, reset network settings and when he inserted the sim back, it shows his number, when he turns on the iMessage and  logs in using his email, it shows my phone number..!
i went to view account, and it redirected to appleid.apple.com and i can see his phone number in the account.
checked the location, set to India, time zone and everything looks fine.
But the Apple ID is remembering my number instead of registering his number..!
BTW, can you elaborate your reply for my 3rd Question.
I've created a contact record with his name, phone number(with country code) and email addresses.
Now what is the next step..?
"setup phone to register with iMessage" can you explain this.
I'm planning to remove sim in my phone, restore it to new device, setup the required softwares etc, take an iCloud back-up and ask him to restore from that backup. Since, the Apple ID doesn't know any phone number, when he inserts sim and turns on iMessage it should register the new number..!