While masculine forms of professions may technically be used for females, the Ukrainian language strongly prefers the corresponding female forms if they exist. The recent trend has been to come up with female forms, which didn't exist in the past.
Can улюблена be changed into влюблена?
No, no в in this case
вона мій улюблений письменник
This sounds quite awkward, but not completely incorrect. I think most people would use feminine form письменниця in this sentence.
Улюблений письменник refers to a male writer. Улюблена письменниця refers to a female writer.
The word "Письменника" exist? If yes, it refers to a feminine form of "Письменник"?