Would someone tell me the name of the lute that appears in the video ? I know of similar looking lutes from Daghestan, Chechnya, etc. but I have never seen one with the supplemental higher pitched string. I would love to find an instrument that's correct for playing certain music from the region.

C. Ewen MacMillan its kemençe the music from northeast turkey

If by lute you mean the instrument at the beginning of the video, its "panduri". The violin-like instrument is "kemençe". It is also known as pontian lyra.

temekki o sendun.Hay gozunden opeyim seni,

bok gibi olmamıış :)

aleynanin koynuna o zaman

Adam du adam adam.