I like Byzantium idea. Good nation to showcase the coalition mechanics, supporting rebels (province flipping). My imagination runs wild. Building the front against the Ottomans with early PU with Naples or other Italian state with good navy, getting big guns like Austria or Hungary into coalition.
Will Byzantium get negative relation modifier for annexing Greek minors?
Precisely. But the coalition mechanics only kick in at Administration level 10 or being the papal controller.
I doubt that, Byzantium has cores on everything in the area, so I find it hard to see any negatives except for the fact that it starts off orthodox.