Does Ender ever directly pilot ships and the Molecular Disruption Device in the book? Or does he just come up with tactics, maneuvers, and issue commands?
Both. During the simulation phase on Eros, he controlled a single ship at a time at first. Then as he progressed, he moved on to voice commands. He tried to control a single fighter when he was commanding multiple, but this failed at first. Although he did end up mastering switching control of a single fighter and commanding multiple, he mostly only commanded the actions, and the pilots (simulated or not) did whatever he ordered, including the other squadron commanders (the other kids) at the final battle.
Gradually, as he became more adept at controlling the fighter's speed, direction of movement, orientation, and weapons, the game was made more complex.
When he had mastered the one-fighter game, they allowed him to step back into the four-fighter squadron. He spoke commands to simulated pilots of four fighters, and instead of merely carrying out the computer's instructions, he was allowed to determine tactics himself, deciding which of several objectives was the most valuable and directing his squadron accordingly. At any time he could take personal command of one of the fighters for a short time, and at first he did this often; when he did, however, the other three fighters in his squadron were soon destroyed, and as the games became harder and harder he had to spend more and more of his time commanding the squadron. When he did, he won more and more often.
At the final battle, although the language doesn't specifically say it, it appears that he is only issuing orders (which makes sense given that real pilots were in the ships).
He whispered quickly into the microphone. His commanders took their parts of the fleet and grouped themselves into a thick projectile, a cylinder aimed at the nearest of the enemy formations.
Ender dodged downward, north, east, and down again, not seeming to follow any plan, but always ending up a little closer to the enemy planet.
This is directly followed from the previous paragraph, so even though it says "Ender dodged", it implies (at least to me) that he is issuing more orders to accomplish his maneuvers
And the finale of the battle was more commands.
Then he whispered a command and the ships dropped like rocks toward the planet's surface. They were starships and fighters, completely unequipped to handle the heat of passage through an atmosphere. But Ender never intended them to reach the atmosphere. Almost from the moment they began to drop, they were focusing their Little Doctors on one thing only. The planet itself.
TL;DR: Ender does not pilot any ships, nor control the Molecular Disruption Device.
When Ender arrives at Command School, he starts by piloting ships, but only in the simulator:
At first, not knowing the awesome power of the game, he has played only at the tactical level, controlling a single fighter in continuous maneuvers to find and destroy an enemy.
But soon he is moved on to higher levels of command (still in the simulator):
When he had mastered the one-fighter game, they allowed him to step back into the four-fighter squadron. He spoke commands to simulated pilots of four fighters […] At any time he could take personal command of one of the fighters for a short time, and at first he did this often; when he did, however, the other three fighters in his squadron were soon destroyed, and as the games became harder and harder he had to spend more and more of his time commanding the squadron.
Once he has squadron leaders to delegate to, he no longer has the option to directly pilot any of the ships:
“But how do I control the ships?” asked Ender.
Mazer explained. He wasn’t going to control ships anymore.
Ender never directly controls the Molecular Disruption Device, in the simulator or otherwise:
“Why haven’t I been trained with this?”
“You always have. We just let the computer tend to it for you. Your job is to get into a superior tactical position and choose a target. The shipboard computers are much better at aiming the Doctor than you are.”
At some point in this process the simulated battles are replaced with real battles, but because the Command School staff are lying to Ender and the other children, it is not completely clear when this switch takes place. Mazer later gives a clue:
“Ender, you never played me. You never played a game since I became your enemy.”
so the most likely point for the switch is where Mazer says:
“So Ender, we will now begin your education. We have programmed the computer to simulate the kinds of situations we might expect in encounters with the enemy. We are using the movement patterns we saw in the Second Invasion, but instead of mindlessly following these same patterns, I will be controlling the enemy simulation.”
If this theory is right, Ender never directly piloted any ships: by the time the simulator was replaced with reality, he had been moved to higher command.