Превод - Турски-Английски - Zeybek Ege Bölgesi'nin dansıdır.Bir veya bir kaç...

Hello kfeto.
"Bir kaç" means maximum 2-3 people.
And..I think "lively" is not enough to express "çok hareketli".

Last sentence...it's too difficult...

The dance is performed alone or with one or two persons. It’s a dance very breezy.
« Mostly one can find it in the provinces of Aydın, Antalya and Balıkesir » here you forgot Izmir.
I agree with cesur the last sentence is a hard one.

added very, few, lively
thank you for the comments

hi kfeto
nice translation
I thought that this might help you with the last sentence.

Just as in the phrase “zeybek outfit” zeybek dance may refer to the dance unique to its performers however, the word zeybek alone is the general name of all its varieties.

Translation of the last sentence doesn't match the exact mean with the original one.
To my thinking, it is better to say:
"As in the expression 'Zeybek Outfit', which refers to the outfit of Zeybek dancers, it is right to call the dance of Zeybek's as 'Zeybek Dance'. However, the word 'Zeybek' itself is enough to refer to a general term of this genre of dance."
or
"It is right to call the dance of Zeybek's as 'Zeybek Dance', as in the expression 'Zeybek Outfit'. However, "Zeybek" itself could be used to depict the dances of the Zeybek's (Zeybek dance)."

i will look at this again tomorrow with a clear head;-) incorporating your suggestions.

In my opinion, it sounds better: 'Zeybek usually performs in the provinces of...'

ok, i think the last line is ok now, thanks everyone for your ideas