If you're buzzing at the 8th fret, you need more bow. Loosen the truss rod a smidge (1/8 - 1/4 turn), then let it sit over night. Retune and check it again in the morning.
I always tweak the truss rod with the guitar at pitch.
How high should your clearance be? There is no "set" number, since all guitars vary a little. .3mm seems a bit on the low side, but again, there is no "set" number. I adjust mine until the buzzing stops.
Try doing a complete setup: adjust your nut height to give you no open string buzz (but get it as low as you can), then your bridge height (get the action as low as you can on frets 12-24 without buzzing), then adjust your neck bow to give you buzz-free action on frets 2-12. You'll be good to go.