I have that very same problem with sleeveless tops.
You can indeed put darts in before you finish off the armholes. Are your armholes to be finished with bias tape, or a facing? If it will be a facing, you will have to make the same dart adjustment to the facing in order for it to fit into your adjusted armhole.
As for the neck line, hmmmm...... I don't think I've ever encountered that problem. But I think the gathering looks pretty cute! The only 2 things I can think of are a) the neck opening really is too wide for you, and you'll have to redraft your master pattern for future attempts, or b) its possible that changing the angle of your shoulder seam slightly will help that excess fabric lay flatter against your chest. Play around with it by pinning a bit and see what happens.
Good luck! The fabic color is very pretty with your skin tone!