I'd like to know if there is a common metalcore approach (like the rules between drum kick and bass, bass and guitar, breakdown) in details.
Vocals are traditionally screamed. Combination vocals started to emerge in the 2000s or so. Clean vocals usually appear in the chorus or the bridge, but any combination can come up.
In terms of guitar, heavy riffs are pretty big. The most common tunings are Drop D, Drop C, and Drop C#. Some bands use Drop G or F#.
Double bass drumming is very characteristic of metalcore. Blast beats involving combinations of bass, snare, and various cymbals are also common.
Specific sub-genres also have their own specific characteristics. Melodic metalcore (ex. Bullet for my Valentine) use more melodic vocals and have more emphasized melodies in general. Mathcore (ex. Dillinger Escape Plan) are generally faster, more technical, and have random and obscure time signatures. Deathcore (ex. Suicide Silence) brings in death metal elements and riffs, and have a stronger emphasis on breakdowns and beat blasts.