How can you improve separation when recording vocals and instruments together?
Believe it or not, modern hypercardioid microphones (if they are positioned correctly) are capable of a very high degree of separation provided that the level of reflected sound in the room is fairly low. This fact can be used to advantage when recording acoustic guitar and vocals together. Aim the vocal mic upwards at about 45 degrees and position it fairly close to the vocalist's mouth so that the singer is singing 'across' the mic capsule; aim the guitar mic down towards the soundhole from a position about three inches away from the soundboard and as near to parallel to the face of the guitar as possible.
Experiment with the precise positions to get the tone/separation which you require. The vocal sound depends on the off‑axis sound of the microphone to some extent, while the guitar sound may be made less bassy by turning the mic so that it isn't pointing directly at the sound hole.
If the vocal sound is prone to popping, put a mesh pop shield between the singer and mic. The degree of separation that can be achieved in this way is rather better than you might imagine, though the use of a compressor is not recommended, as this swill adversely affect separation.