merhaba!

i wanna ask you what is the meaning of Ellerinize Sağlık?

and which one is true? Ellerinize Sağlık or Ellerıne Sağlik?

teşekkür ederim 

I think both ways are correct. Maybe ellerinize sağlık is more formal.

I´ve heard people say it as congratulation on good cooking. I don´t know if it´s used in other context.

Yes, we use that in other context too. To say our thanks to someone who made efforts by doing something for us.

you can say it to a plumber who fixed the tap in the bathroom.

to an electrician who fixed the electric problem in the house.

etc..

thank you so much guys!

It hinges on you how to conjugate.

el (hand), sağlık (healthy)

It is optional to use "el" in singular or plural form. Makes no difference.

Eline sağlık. (I liked what you cooked/made.) (purely: Healthy to your hand./hands. so that you can go on cooking/making such these.)

/Ellerine sağlık.

el+n(possessive of 2nd singular)+e(dative)--->eline

eline sağlık (healthy to your hand)

el+ler(plural)+n(possessive of 2nd singular)+e(dative)-->ellerine

ellerine sağlık (healthy to your hands)

el+niz(possessive of 2nd plural)+e-------------->elinize

In Turkish, the second plural is also used in respectful expressions. For example to the teachers, to the formal people, to the people who don´t know. If these people whom you are not sincere are about your age, it is not very necessary. But if they are much older than you, you must use.

for problems about possessives:

http://www.turkishclass.com/turkish_lesson_259