The answers to this long list of questions is much more than just a few equations and defined variables.  Most of the calculations are interrelated, where one selection or set of conditions recommends a direction to use other calculations and correlations.  These questions can only be answered by understanding and following a design procedure.  The following articles provide a basis for most of the calculations you have requested:
Hicks, R. W., Morton, J. R., Fenic, J. G.,
How to Design Agitators for Desired Process Response,
Chemical Engineering, April 26, 1976, pp. 102-110.
Dickey, D. S., Hicks, R. W.,
Fundamentals of Agitation,
Chemical Engineering, February 2, 1976, pp. 93-100.
Dickey, D. S., Fenic, J. G.,
Dimensional Analysis for Fluid Agitation Systems,
Chemical Engineering, January 5, 1976, pp. 139-145.
These articles and similar ones provide a basis for the design of liquid mixing equipment.  The articles have correlations for impeller power, mixing intensity, baffle recommendations, and other design information.
If you need more information, I suggest that you obtain a copy of this handbook:
Handbook of Industrial Mixing, Science and Practice, Editors, Paul, E.L., Atiemo-Obeng, V. A., & Kresta, S.M., John Wiley & Sons, Inc., Hoboken, NJ (2004).
A simple question with a reasonable answer, which is hidden in your long list of questions might be, "How do you compute impeller power for a pitched-blade turbine in turbulent conditions?"  To which the answer is Power = Power Number times Fluid Density times Rotational Speed cubed times Impeller Diameter to the fifth power.  Of course you need to work in coherent units, such as power in Watts, power number is dimensionless and about 1.37 for a pitched-blade turbine, fluid density in kilograms per cubic meter, rotational speed in revolutions per second, and impeller diameter in meters.  The effect of viscosity is included in other correlations for power number as a function of impeller Reynolds number.  You should be getting the idea that the questions you ask are more than just simple equations and calculations.
I know that this brief description does not answer all of your questions.  However, if you want to do mixer design, you will have to do some investigation and research.  It takes a 1,600 page handbook to begin to describe what is known and influences mixing.

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