The Turkish campaign of 1787 is set off when Catherine's ambassador is imprisoned at Yedikule Castle. In fact, that incident set off the Turkish campaign of 1768.
Paul never marched his army to Catherine's palace to prove to her his desire to fight the Turks. She did allow him to participate in the Russo-Swedish War (1788-1790), but not in actual combat.
Catherine would never have attributed the creation of the Russian Empire to herself.