When you are trying to do small scale mixing studies you need to be creative and look for companies that specialize in small-scale mixing equipment and tanks.
The first question is relatively easy.  The depth and shape of the bottom is not usually critical.  However, if the bottom is dished, such as an ASME dished head, then you should test in a tank with a dished bottom, not a tank with a flat bottom.  If the dished head is deep, such as a 2:1 elliptical or hemispherical head, then a deeper dished bottom may be needed for the test tank.
Small pitched-blade impellers are probably expensive in your mind, since size does not have much effect on the labor required to make one.  A small impeller requires about as much time and effort to make as a medium size impeller, so a 6" diameter impeller is not going to cost much less than a 12" diameter impeller.  It all depends on what you think is expensive.
Several companies specialize in small mixers and impellers, such as Mixer Direct, Indco, and Prop-r-mix.  I am sure you can find these and other companies on the internet.