Is the energy density of vacuum uniform in the whole universe?

The simple answer is that we don't know that dark energy is uniform on any but the largest scales. The only evidence we have for the existence of dark energy comes from:

Both of these measure on scales far larger than galaxies. The resolution is more like 100 to 1000 million light years than the size of a galaxy. In any case it would be hard to measure the effects of dark energy in anything smaller than galaxy clusters since these are gravitationally bound and the effect of dark energy would not be easily measurable. I confess I'm unsure to what extent the effects could be seen on the supercluster scale.