Hello there! I'm sure someone a bit more experienced than me will respond, too.
For now:
Are you noting the shape of the fretboard with the strings depressed at various high/low frets? If not, fretting a string at the 4th/16th fret (for instance - can be moved up/down and lengthened/shortened) creates a straightedge from which to gauge neck relief.
If you did, though, I would say that you need to tighten that rod to level your neck out.
Then, address your 4th/5th fret buzz. Double-check that straightedge string along the neck (heck if you have a straightedge, toss that on and see!), it may be that you're over-tightening the truss rod and introducing the fret buzz.
If not, sight along your neck as well as fretting around the neck to gauge your action. Your saddles may need to be raised but keep your eye on your action. Raising your saddles will introduce higher action at your higher frets but may remove the 4th/5th fret buzz.
If it does, then your frets up there may be popping up or may be higher than your other frets. Otherwise, your nut's grooves may be worn deeper than spec, lowering the strings at the nut-end of the fretboard while causing no playability issues higher on the neck.
Complex, but step through and you may find yourself in a much better position as far as dealing with your buzz!
