Stirred, not shaken! Shaking is fine for paint thinned to spraying viscosity, but for brush painting, stir, never shake. However, if the paint is at proper viscosity for brushing, the brush painting process will cause the bubbles to break unless the paint is too viscous and the coat too thick.
Now old are these paints? All paints lose solvent over time, especially enamels and lacquers. It needs to be replaced. For enamels, mineral spirits is the best choice. For lacquers, lacquer thinner.
It looks like there are small lumps in the paint, either undispersed pigment or partially cured binder, the latter of which can occur in old paint and will not redissolve. They have to be strained out through a fine screen, or the paint should be discarded and replaced.
When storing paint, make sure the top and threads of the jar are clean, remove any paint on the lid seal, and tighten the lid as tight as you can get it with hand strength. Don't use pliers, they will distort the threads on the lid.