Proper passenger train braking procedures

When a train is stopped at a station, must the brakes be in full service? For locomotives with manual lapping brakes, how much air must be set?

Also, when slowing a train down or bringing it to a stop, is there a recommended time to wait between each brake application? Or is it okay to apply as much air whenever possible?

Braking for a passenger stop has a lot of variables. You have to take into consideration the grade, number of cars, speed on approach, weather and other factors and still give passengers a smooth stop. I don't think I ever used full service. On the F7's and GP9's I operated, we didn't have graduated braking where you can do a partial release. So you wanted to use minimal braking otherwise you had to do a full release or apply more power and hope you didn't pull them apart.
On modern equipment you can do a partial release which makes a smooth stop much easier.

I was always taught when stopped at a station you should have the automatic brake valve in suppression, the independent fully applied and the throttle in idle. Never run a train with a manual lap brake but the above should hold true whether in direct or graduated release.

When it comes to stopping the train direct release or freight brake vs. graduated release or passenger brake are two completely different animals. As explained above, with direct release you could in theory make a 10lb reduction then manipulate the throttle back to idle to make your stop possibly adding a little more air as needed. This type of braking in modern passenger service is frowned upon except in very few places like Auto Train.
Graduated release allows you to manipulate the brake to add and subtract air to make you stop. But air on a train is not a constant. The more you manipulate the brake valve the less air you have in the system.
Then of course there is a third option called dynamic braking for slowing your train if the engines are so equipped.