1. A double pole 15 amp breaker that matches your panel.
2. 14/2 cable will be fine you don't need a neutral so the white can recoloured to black.
3. Yes only two wires are needed plus ground.
4. Does the compressor have a plug? That is all you need.
5. 1/2" will be fine for #14. You will want THWN wire not cable in the conduit. Get enough black for both runs or a red and black. You can't use white in this case.
2. 14/2 cable will be fine you don't need a neutral so the white can recoloured to black.
3. Yes only two wires are needed plus ground.
4. Does the compressor have a plug? That is all you need.
5. 1/2" will be fine for #14. You will want THWN wire not cable in the conduit. Get enough black for both runs or a red and black. You can't use white in this case.