Hi

I don't know about others, but generally, if you have already glued in the nut, you adjust the nut by filing the string slots. Again, I don't know about others, but I adjust this by fingering the 3rd fret and seeing what the gap between the string at the nut and the 1st and 2nd frets are. It should be just off the frets. When filing the slots, you might want to put some tape on the headstock to protect it, because you should file at an angle similar to the angle of the strings from the nut to the tuners.

As for keeping in tune. it's usual practice to stretch the strings by gently pulling up on the strings before you go to full tension. Others here may have different ideas. pay attention to them all and decide what you wanna do .