I press when machine piecing, usually with a dry iron. When I was a beginner I used a steam iron, but eventually realized that I am more accurate with a dry iron.
Having said that, I have read on the QB about people who have taken a class from Kaye England. If I understood those posts correctly, she does not press until the top is finished. I remember one post especially about a student who tried this out for himself and said he got better results with it. I haven't had the courage to try it myself.
As for starching, I do not prewash fabrics so there is enough stiffness in the fabric to give me accurate cuts. If I do have to prewash a fabric for some reason (if it does not pass my colorfast testing, for example) then I always starch the washed fabric before cutting to restore some crispness.
If I know I will be sewing long bias seams, then I heavily starch the fabric before cutting to keep the fabric stabilized while I work with it.
There are different ways to starch. I reserve spray starching for finished tops because overspray isn't such a problem for me then. If I need to starch yardage, I mix a solution of Sta-Flo liquid laundry starch and water, "paint" this on with a large wall painting brush, allow a couple of minutes for the starch to be absorbed, toss in the dryer, and then iron with steam. This is much less work than trying to spray starch yardage.