Is space expanding equally in every direction? Does space expand equally in every direction, so that it draws a perfect sphere or is expansion asymmetric, so it creates "bubbles" (when seen from the outside)?
 A: In the Friedmann Lemaitre Roberston Walker universe, the space-time is expanding expand equally in every direction of space. Cosmological studies suggest that the universe is flat and it is believed that matter structures have grown from the stage when they were in fact small deviations from local equilibrium (they were local instabilities) and by gravity effects they grew to big matter structures. The universe have developed in certain stages. 
A: The current accepted cosmological model is called $\mathrm{\Lambda{}CDM}$, and one of its basic assumptions is that the universe is isotropic. This assumption is refered to as Cosmological principle, and if true, then the rate of expansion must be equal in every direction (the "bubbles" you speak of exist at galactic scales, but not at cosmological scales: the universe, seen as a whole, is very smooth). In the model, the expansion rate (scale factor) is $a(t)$, which is position-independent. For more details, see Friedmann–Lemaître–Robertson–Walker metric.
The universe expands isotropically, but it doesn't mean that it "draws a perfect sphere": the universe does not expand from a point. For more details, see What is our location relative to the Big Bang?.
A: This question is somewhat difficult to answer without first digressing into the so-called Friedmann equations. These are the equations on which modern cosmology is built. The Friedmann equations themselves assume three things:

*

*General Relativity. Shouldn't be surprising, since that's our prevailing theory of gravity.

*Isotropy. This is the idea that the universe looks the same in every direction.

*Homogeneity. This is the idea that the universe looks the same regardless of where you set up your telescope.

In this context, the question "is space expanding equally in every direction?" is effectively equivalent to "is the universe isotropic?". The answer to that is yes. This is the most recent paper I've seen on the subject (although I've not conducted a more recent literature search).
That said, nobody expects the universe to be completely isotropic. After all, the universe is clearly not isotropic on solar system scales. When put this way, the universe is obviously not expanding equally in every direction. The question becomes "how large are the deviations from isotropy?", and that is a different question that's potentially measurable. There has been no detection yet (c.f. the paper linked above), but you can be sure that if anisotropy is detected, the results will be significant.
