Can protein precipitate out in alcohol during DNA extraction? In common lab sessions to extract DNA from strawberry or cheek cells, will there be protein contaminating the DNA extract in alcohol? If so, how can we prevent protein from precipitating out of the solution?

Yes, Ethanol can precipitate proteins during a DNA precipitation as well, although Acetone will be more efficient. Usually you do a proteinase K digest or a proteinase K digest followed by a Phenol/Chloroform extraction to avoid this problem. I was usually doing the later, I can post my protocol if you are interested.