I driven a lot of miles in a manual and I almost always sit in neutral with the clutch out and my foot on the brake petal. Whether this is correct or not for all situations, I don’t know but that’s my habit.
As for taking your foot off the clutch petal, I think you may have poor communications from the pro instructor and I lay that on him not you. I think he wanted you to completely remove your foot from the clutch petal between gear shifts and certainly once you are cruising along in top gear. The saves wear and tear on the clutch.
If you take your foot off the gas completely between gears you could get some “herky, jerky” shifts. You want to let off the gas enough to drop the motor rpm’s about 800 rpm between gears in a Honda. Then when you let out the clutch you should not feel any jerky action from the car. Do what makes for nice smooth shifts. You will learn to get smoother with time and practice. Use your “ears” to judge the motor speed and seat of your pants to feel how smoothly you are shifting. If your passenger’s head is bouncing around like a bobble head doll your technique needs some work.
Sometimes when you need to get on the gas and accelerate quickly to get in front the semi as you enter the interstate; smoothness goes out the window and you just let 'er rip and throw some “power shifts” as fast as you can. Different driving situations dictate your shifting patterns making any hard and fast rule pointless.