For the conquest of Constantinople, the best recent work is Jonathan Harris, The End of Byzantium (Yale University Press, 2012). There is also Marios Philippides and Walter K. Hanak, The Siege and the Fall of Constantinople in 1453: Historiography, Topography, and Military Studies (Ashgate, 2011), but that one is much denser, clearly intended for a more "academic" audience - it has a ton of information, which is great, but it's a bit overwhelming sometimes. Harris' book is more readable, certainly.

Of course there is also Steven Runciman, The Fall of Constantinople, 1453 (Cambridge University Press, 1965). As with all of Runciman's works, I would describe it as very readable, but very out of date. Better to stick with Harris.

As for Mehmed, as far as I know, the translation of Babinger's biography is the most recent one in English.