Definitely a difference in gripped and ungripped, and also a difference depending on the grips. A midsize will read different than a standard grip, a cord grip will read different than a rubber grip. What you see on a chart depends on if the chart was designed to read gripped clubs or ungripped clubs. Our GLFMC chart is basically for gripped clubs. We put together some charts for ungripped clubs, showing the ranges in flex designations you can get due to the differences from one manufacturer to another. The link is below:
Clamping pressure and clamping dimension can also effect what kind of readings you are getting. If you have our Frequency analyzer, the clamping dimension is 5″ and the clamping pressure is controlled, so there should not be any variance there. Jim and I tend to like to use the ungripped charts to get a better idea on the frequency. It eliminates the inconsistencies in how the grip can effect the reading. That being said, and I always remind frequency machine users, that frequency is not flex. It is a comparative measure of a shafts stiffness when oscillated, but does not account for variations in the flex profiles of shafts. It tells you how a shaft oscillates and the relative stiffness of the shaft in that mode of measure. It does not tell you how the stiffness may vary in the mid section or tip section of the shaft. That is why you can have 10 shafts that have the same butt frequency when clamped into the 5″ clamp and oscillated, but none of them play or feel the same. I still think it is a viable way to get an initial comparison of shafts, but just be aware of what it is, and what it is not, telling you with the numbers.
Your assumption is correct. A gripped club will measure 6-12 cpm less than a gripped club.
You would need to remove the grip in regards to your second question.