First British passport application and signature

[voyager1]

I have a few questions regarding the Certificate of Entitlement to the Right of Abode.

I recently had my British Citizenship Ceremony done outside the UK and received my British Citizenship certificate. I have a couple of questions regarding the COE:

1- When applying from overseas, is it quicker to receive a Certificate of Entitlement than it is if you apply for a British passport for the first time? How long does it usually take to receive a Certificate of Entitlement after you have made your application for it from overseas(outside the UK)?

2- After I have entered the UK with a Certificate of Entitlement, will it be easy for me to get things like a national insurance number(because I want to work in the UK as quickly as possible)?

[voyager1]

I have recently had my British Citizenship Ceremony done overseas. I have a question about applying for my first British passport.

On the application form for a British passport, it requests that the applicant must write down their signature. My question is does my signature for my British passport have to be the same as the signature on my non British passport(I have a Bahraini Passport)? Or can I write down a completely new signature on the application for my British passport? I would of course also use this new signature to sign on my British passport when I eventually receive it.

My signature on my Bahraini passport is in Arabic, I would like to use a new signature that is in English for my British passport.