Hi,

I will try to be as brief as possible and not leave out any information

So the current situation and background is:
I am a Hungarian citizen, 37, living and working in the UK for the last 4 years.
I am with my current employer for almost 2 years.
I am working on an hourly rate of 7PPH as a Security Officer in a school, which means if a month has school holidays my salary is lower than usual (especially in August).
I am living in a Shared (Terraced) House, in a separate room, about 6 square meters plus a 2 square meter storage area. Both spaces are exclusively accessible by only me. There are 5 rooms, with 5 other tenants, 1 bathroom, 1 kitchen.
My wife is a Filipino citizen, 19, living in General Santos City, Philippines. She just finished studies and not working at the moment.
We got married on 11th of November, 2012.
I've visited her and her family 3 times for 16-21-21 days.
We have a chatlog of around 300'000 messages only on Facebook Messenger (no kidding ) and around 100'000 messages on Skype (unfortunately no logs available of the Skype Messages) and about 5-600 pictures and few videos together.

So we just got to the point where I have enough funds to bring her over here but browsing all the sites about information is just left us confused

So my questions and concerns are the following:
- First of all...
= Do we need to 'inform' any office here in the UK about our marriage? I have an original copy of the Marriage Certificate.
- As I am being a EEA national we can apply for the EEA FP.
= Should I apply in the UK for her Entry Clearance or should she apply for EEA FP in Philippines?
= What are the costs involved in one or the other way and what are the usual average processing times?
= With my shared accomodation, my not too high (average Net 1000 PPM) income do we have a chance?
= With the quite big age gap (18 years) and she being quite young (19 years old) could we face problems?
= I am receiving Working Tax Credit. Is it considered as a Benefit or kind of dependancy on state funds?

- Once we have the EEA FP...
= Should I travel to the Philippines to 'pick her up'? I am just very worried if anything happens at the UK border she would be alone... but financially it's not easy...
Can she apply for an NI straight away?
= How long she can stay without the need of renew the 'Visa'?
= Can she travel within the EEA freely if she travels with me?
= Does she needs any extra permit to start working?

I am sorry for having so many questions, but in the maze of internet I got lost already and we just want to be together finally but feels like we have to overcome many buerocratic walls before we can finally live our life as a family.

Thanks for everyone who can give us advice or just point at the right direction