What was the role of the Turkish language in the Balkan sprachbund? How was Turkish affected by it or how effected it?

All Balkan languages have borrowed substantial Turkish vocabulary, and all Balkan languages have borrowed some Turkish affixes.

However, the Balkan Sprachbund is defined through the convergence of grammars, rather than just their borrowings from a common source. It is defined by shared morphological categories and syntactic constructions: a convergence such that, if you replace a Greek sentence with Albanian, word for word and suffix for suffix, the results will more or less make sense.

In that regard, the contribution of Turkish has been marginal. The “supposedly” suffix of Turkish, –miş, counts as a new morphological category, and has found favour in at least one dialect of Aromanian. That instance aside, the morphology and syntax of Turkish have remained quite distinct from that of the Balkan languages. (What happened to Greek in Anatolia was a different story, but it does not count as Balkan.)