Hi Murat
Please notice that when oil passes through a small hole it will for a short period be subjected to high shear. If the oil contains VI-improver that will be a problem because the high shear will cause both a temporary and a permanent viscosity loss (break-down of the VI-improver). The best solution is to use an oil which has no VI-improver, but preferable with a high natural VI. A high natural VI is normally obtained by using PAO, ester and/or Group III base oils.
There is probably a relation between the oils viscosity and the level of vibrations/noise. Oils with higher viscosity (and/or no break-down of the VI-improver) will often reduce vibrations/noise.
The problem with foam is more complicated and I am not sure that you can solve it with focus on the fluid only, you will probably also have to take a closer look at the construction.