Learn Turkish: Vicdansız bir adam tutkusuz bir kadını sevebilir mi? - Can a ruthless man love a passionless woman?

The privative suffix -sIz follows 4-way vowel harmony. The last vowel in vicdan (conscience) is 'a', so it takes -sız. The last vowel in tutku (passion) is 'u', so it takes -suz. Literally, these translate to "without conscience" and "without passion."

Why does kadın have the accusative ending -ı (kadını) if the sentence says bir kadın (a woman)?

Normally, indefinite objects with bir don't take the accusative. However, the verb sevmek (to love) strongly prefers a specific direct object. Also, adding a descriptive adjective like tutkusuz before bir makes the object feel more like "a certain passionless woman." In Turkish, this makes it specific enough to require the accusative -ı.

Could I change the word order to bir vicdansız adam instead of vicdansız bir adam?

You could, but it changes the nuance slightly. Vicdansız bir adam is the standard way to say "a ruthless man" in Turkish, putting the focus on the adjective. Saying bir vicdansız adam sounds more like "one ruthless man" or treats "ruthless man" as a single inseparable concept.

What suffixes are making up the verb ?