The white lines are probably residue from your guitar polish or something. Can try using a soft bristled toothbrush to brush it clean (brush lightly along the grains). I guess it's ok for the fingerboard to be dry. Actually, the dryer it is, the better it vibrates? Some ppl like to put lemon oil on the fingerboard to keep it moist and smooth, though.
Another thing with replacement necks is to ensure that the string length is correct. I haven't replaced my necks before so can't tell you much but my guess is that if the string length after installation is not right, your intonation may go haywire, perhaps out of the limits of your brigde adjustments.
A safer bet would be to redress the frets or refret, the later costing more. But there's less chance of screwing up the guitar.