There is a close relationship. The oil temperature increase as mentioned above lowers an oil viscosity (viscosity is halved when oil temperature increases by 10℃) Thus, when a piping connection is loose, oil starts to leak out. For the early stage of leakage, cleaning oil to lower the oil temperature should prevent further oil leaks.

Air bubbles are introduced when strainers and/or filters are clogged or the piping connection loosens, causing suction of air. Clean the strainers and filters, check and retighten the loose piping connection between the oil tank and the pump.

No, the viscosity does not change.
You should not check the viscosity of oil in use by fingers. It must be measured at a constant temperature. At the plant, one measures viscosity of new oil when it is cold, and oil in use when it is hot, which is an obvious reason why the oil viscosity seems to have changed.

Since oil is a pressure transmitting medium for the hydraulic machine based on Pascal’s principle, the color is irrelevant. The color changes are due to oxidized products reacting with very small amount of nitrogen compounds in oil (a few tens to a few hundreds of ppm) resulting in coloring. Therefore, there is no alteration in basic properties of oil.