I am trying to wire a duplex receptacle with one half of the receptacle controlled by a switch (half-hot) and the other half by a GFCI.

My approach is: 1) Break tabs on both sides of this receptacle. 2) using a 14/2 from Load side of GFCI to the bottom-half two screws of the receptacles 3) Using a 14/2 from a single pole switch to the top-half two screws of this same receptacle.

Would that above approach work?

Only if the switch has power to it.

Power from 2 different branch circuits feed GFCI receptacle & switch separately. How to wire GFCI and switch from panel?

Are you asking how to wire two circuits to a split receptacle or are you asking how to wire a split receptacle after a GFI.

Logic tells me that if one half of a receptacle needs to be GFI the other should be also.

I am looking to split receptacle half-hot controlled by a switch and the other half protected by GFI, which should be from a different circuit.

Well, it can be done, but why? The correct way would be to build a switch loop from the lower receptacle (hot) side to the switch with a return to the top brass screw.

Normally, since this is a duplex receptacle you draw power from the constant on receptacle and feed the switch which in turn controls the top circuit.

You accomplish this by breaking the brass side tab and leaving the silver tab connected.

You would build the switch leg by connecting the white feed the switch from the pigtail for the lower receptacle. Connect the black from the switch to the brass screw on the receptacle top. Marker the re-tasked white with either black tape or magic marker at both the receptacle and the switch. At the switch, connect the white to the lower screw on the switch and the black to the upper screw on the switch

The method you originally described will work.

Again I ask, if one half of the receptacle is GFI protected shouldn't the other half be also.

Is there a real need for each half to be a separate circuit? If not wire as Don described.

The receptacle is currently protected by GFI. I want to create a switch to control the lamp in this room.

Turn off power to circuit.

Remove receptacle from box.

Remove hot (black) wire from receptacle.

Break tab between hot (brass) terminals of receptacle.

Using a wire nut, connect hot (black) wire to white wire of cable going to switch and add a pigtail.

Connect pigtail to one of the hot (brass) terminals of the receptacle.

Connect black of cable going to switch to the other hot (brass) terminal.

At the switch, connect the black and white wires to the switch terminals. It does not mater which wire connects to which terminal.