Dear Fedaykin,
American interest in Central Asia is not a secret. The latest “new cold war” talks we had seen on the news last weeks is a reflection of this interest which is the main tool of USA to block the monopoly Russia has in natural gas market. Turkey is once again the most favorable ally of US in this scenario, having ethnical & cultural ties with these Central Asian Turkic States. According to the recent developments, both Khazak and Turkmen gas/oil will flow thru BTC pipeline into Israel and Europe. So it is not surprising to see increased US presence in Caspian region which will seriously bother Russia and Iran.
As for your Turkish ship building question, i am definetly not the most knowledgable person here about this matters. I personally know some Turkish members of this forum with much greater knowledge in the matters, however i am not sure if the forum allows pure navy topics anymore.
The corvert you mention is MILGEM Patrol and Anti Submarine Warfare Ship. Besides Pakistan , Ukraine is also said to have interest in the project.