Learn Turkish: Sürekli eski sevgilisinden bahsetti, ayrıca çok kibirliydi. - He constantly talked about his ex-girlfriend; furthermore, he was very arrogant.

Yes, you could definitely say üstelik çok kibirliydi. Both ayrıca (furthermore) and üstelik (moreover) are used to add a piece of information that reinforces your main point. Here, they both work perfectly to pile on another negative trait about the date!

Why does sevgili have the ablative ending -den (sevgilisinden) if he is talking 'about' her?

The verb bahsetmek (to talk about, to mention) always requires the ablative case (-dan/-den). Think of it as words or information coming from the topic you are discussing. In Turkish, you don't talk 'about' someone; you talk 'from' them.

Can you break down the suffixes on sevgilisinden?

Sure! It breaks down like this: sevgili (partner) + -si (his, 3rd person possessive suffix) + -n- (a buffer letter always used after a 3rd person possessive suffix before adding a case ending) + -den (the ablative case required by the verb).

Why is there a -y- in kibirliydi?