He then studied alongside his brother Johann Philipp Franz at Würzburg, Mainz, Aschaffenburg and Rome (Germanicum).
He also supervised the construction of the Imperial Chancellory Wing of the Hofburg Palace in Vienna (1723–30) by Lukas von Hildebrandt, where he lived in an apartment.
As his private country resort near Vienna, he built the Blauer Hof Laxenburg (1710-1720) and also the Schönborn Palace near Göllersdorf in Lower Austria; there he also purchased Weyerburg Castle.
Friedrich Karl's opposition to the Pragmatic Sanction, as well as his frequent absences from Vienna, caused him to lose influence at the court after 1730.
[2] When the cathedral chapter of Würzburg elected a new bishop in 1724, they rejected Friedrich Karl, due to the unpopularity of his brother Johann Philipp Franz.
In 1724, Friedrich Karl became Dompropst at Würzburg and upon his uncle Lothar Franz' death on 30 January 1729, he succeeded as Prince-Bishop of Bamberg.
Friedrich Karl had been the favourite nephew of Lothar Franz, who bequeathed to him Schloss Weissenstein, a large Baroque palace at Pommersfelden.
[2][1]: 20 As an imperial prince, Friedrich Karl remained a supporter of the Habsburgs, despite numerous and significant political differences.