As per message 12. You need to change every password that you use and in particular if you use the same password on multiple accounts.
You also need to check that there are no forwarding addresses set up in your email account.
As regards what the scammer knew about you.
You have probably posted your name, address, post code and phone number(s) on any number of web sites such as Amazon or other retail sites.
As regards the PIN and email and text being sent to you. That is done by BT when ever you try to change your password using the forgotten password link on your email or MyBT accounts.
The scammers know this and if the have your BT email address, which will no doubt have been used all over the Internet, they simply try to log into your email account and click the forgotten password link and you are sent the PIN.
They immediately call you and stated the have just sent you a PIN to verify that they a genuine BT representative. You then supply them with the PIN to verify to them that you are the recipient of the PIN and they now have access to your account using the PIN.
When you asked for the account number, if you had already given them the PIN they would have accessed your account and been able to recite that back to you without any problem.
You can check to see if your email address has been subject to any data breaches using this link
Have I Been Pwned: Check if your email has been compromised in a data breach
No legitimate company will call you to tell you there is a problem with your Internet or computer or ask you to install anything or give them access to you computer. The only time that might happen is if you call them to report a fault and even then I would not allow it.
Treat any cold callers as scammers and hang up. If they are genuine they will call you back. Ask for a reference number and tell them you will call them back. Use a trusted number to do that, not one that they supply to you.
Never give out any PIN number unless it is in response to something you initiated.
Age has nothing to do with it. More young folk get scammed than the elderly.