1. Cut narrow, boost wide, why?
The reason you cut frequency content is to remove a problem frequency. This problem frequency may be causing phasing, masking, detuning or resonance. Typically, problem frequencies can be carved out using narrow Q values.
Boosting frequency bands with a wide Q value changes the tonal balance in a sound. When using narrow Q values to boost, resonant frequencies can be created and cause problems during mixdown.
2. Remove unwanted frequencies; HPF and LPF, why?
Frequency content outside of 20Hz – 20kHz is often created as a by-product of digital signal processing. This frequency content albeit inaudible, will begin to use valuable headroom. It is important to remove such frequencies to maintain optimal headroom while creating sonically cleaner sounds.
3. Share the frequency spectrum, why?
Instruments can become audibly buried behind sounds of similar frequency content. Scooping favoured frequency bands from opposing tracks will help your sounds mix together better. For instance, if I have 2 sounds being played together and I like the tonal content at 500Hz of track 1, I will scoop out 500Hz in track 2 in an attempt to carve a space for the sound.
EQ is one of the most powerful tools in sound design and mixing, hence why it is generally the first step in most processes. Try to avoid what an EQ looks like and focus on what it actually sounds like, after all...it's our ears we are trying to please!