#1
and i can't lower my bridge any more.
i checked the relief at the 9th fret by barring the first and 24th frets. and there's about 1 or 2 milimeters gap

should i tighten the truss rod a 1/4-turn? or will that throw off the relief?
#3
typically it requires a truss rod adjustment, but usually you need to re-intonate it as well. Raise up your bridge a little, too, or else it might buzz.

If you feel uncomfortable with that, you might want to take it to a shop.
#4
File your nut, adjust your truss rod.
...
Please do not insinuate anything sexual from that.

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