Ä is pronounced as æ/ə and ö is œ, w could be u or ü, lastly x is h. If writing Turkish correspondents will be helpful
Färhät > Ferhat
Gölçäçäk > Gülçiçek
Möxämmät >
MuhammedXämzä >
HamzaZäynäp >
Zeynep Zöläyxa > Züleyha
Firüzä >
Firuze
I don't have information about other names but I think
Lälä is
Lale and Ğäyşä is
Ayşe.