1) I bought a bottle of touch-up paint from the dealership; I applied the touch-up paint three days ago and this is how it looks. Is this how it suppose to come out? Do I need to follow up with a wax? Should I apply some clear coat?

That'* what my touch up areas look like too. The paint on your car was reduced down and sprayed on thin, the touch-up is a thicker layer of paint and will be a more true (darker) color

Evenually it should fade a little and not be so noticeable if at all.

Thank you for your help

Try some hand polishing in that area to help blend it all together. If the touch up is a bit higher you can try wet sanding with no less the 2000 grit.

In my case, I made sure the touch up paint had cured all the way, then sanded it with 2000 grit sandpaper and a wet polishing compound until it blended better.

I've found that, if you have the time and inclination, buying a spray bottle that matches your finish gives a better look than the touch up pens/brushes. It'* a lot more work -- finding a clean space, masking, priming (if needed), doing multiple layers, clear coating, and buffing the final product so it blends in, but the results are totally worth it.

On the other hand, if it'* just a rock chip or something simple like that, the touch up pens probably waaay easier.

Funny thing you metion the a spray bottle, the guy at the GM dealership said that they sell a spray can but no one ever asks for it. I think I am going to go back and get a can try it out on the hood...