I think Pregnancy "Morning" sickness is so unpredictable and that there really is no norm as to when it starts and/or when it finishes when depending on each individual. Yeah, there's a "majority" or "most of the time", but, during pregnancy, I think the Unexpected should be Expected.
I also believe that when feeling ill during pregnancy, you should eat what sounds good to you. Why eat something that may be totally healthy for you yet make you feel soooooo sick? If you haven't been feeling well but a grilled cheese sandwich sounds so much better to you than a piece of baked chicken, go for the sandwich. Once you start feeling better, I would then focus on eating more healthy & getting those much needed vitamins in your system.
As for how often should you eat??? Make sure to keep something on your stomach at all times...whether it be crackers, a piece of dry toast, a handfull of almonds, etc. An empty stomach makes "Morning" sickness so much worse.
And please don't forget to drink a ton of water. The water will help with the headaches.