Firstly, some general answer on nondimensional groups such as the Reynolds number e.g.: they do not generally characterise the flow as a whole, but a feature that you choose in the flow. If the flow is not an academic problem, you will have several such features, which have different lengths, velocities...
In the case of multiphase flow, this is obvious since you already have to choose between two different densities and viscosities, and in your case of liquid+gas they are orders of magnitude apart.
Your aim in calculating the Reynolds number is to evaluate the importance of inertial effects vs viscous ones: thus, for inertial effects, you should probably take the highest density, the one of the liquid. But then, of course, the characteristic velocity you take should also be characteristic of the liquid phase. 568
All this to say that there is no definite answer in general, tell us about your setup and then the discussion can take place.
Concerning turbulence, the Reynolds number at transition is well characterized only in a handful of setups, you'll only have some gross estimate and then have to describe your flow in order to assess whether it is turbulent or not.
EDIT CONCERNING THE APPLICATION
In the case you mention, the Reynolds number in cement is probably quite low, as I guess the viscosity of the cement is high (please provide data). The gas flow might reach higher Reynolds, as here you do not have a suspension but rather a system of cracks, I would use the maximum crack width, gas speed and kinematic viscosity. This will probably be much higher than the Reynolds in cement.
For the numbers you give, the Reynolds number will clearly be low both in the cement phase, as the velocities there will be less than gas and viscosity is high, and probably low in the gas phase, but you don't give an order of magnitude for the width of your cracks. Anyway, for centimeter-sized cracks Reynolds would be of order 10 (although if your gas has very low viscosity that could be much more!) So you'll be able to focus on the complicated problem of Bingham flow plus free surface without having to worry about turbulence. 568