Yes. You must lift the clutch slowly. If its too fast the car can jump about and potentially stall. Depending on where you are the stall can become dangerous.
It for sure depends on the type of car u are driving. Sometimes more gas can be a bad thing because once you lift the clutch the car can lurch forward. If the clutch is down the amount of gas doesnt make a difference as the car will not move until the clutch has gone past the bite.
Clutch out slowly and apply as much acceleration to stabilise the engine revs against the car's speed. The Syncromesh will manage the rest. Older cars don't have this technology and if you didn't do this and double declutching, they would appearently spin out of control.
In a petrol you have to give more gas, otherwise you'll stall. It's probably easier to change gears and release the clutch when already moving as opposed to when you're stationary.