galaxy - Are galaxies moving away from us faster than before?

The recessional velocity $v$ of an object depends on two things: firstly it depends on how faraway an object is in terms of proper distance $D$ and secondly on the rate of the Universes expansion as a function of cosmological time $t$, which is best expressed as the Hubble parameter $H(t)$. Specifically:

$v = D times H(t)$.

It's worth noting this equation is slightly vacuous as it is merely the definition of recessional velocity, which is not something that can be directly measured.

As recessional velocity depends not just on a function of $t$, but also on $D$, the question as to whether objects are receding from us faster than ever before could be answered in several ways. Before I look at the different ways we could answer your question, I will note a few things. Firstly the definition of the Hubble parameter is:

$H^2(t) = bigg( frac{dot{a}(t)}{a(t)}bigg)^2$

where $a(t)$ is the scale factor which describes how the scale of the Universe changes with $t$ and $dot{a}(t)$ is the first derivative of the scale factor with respect to $t$. Due to cosmological observations the Universe is said to contain dark energy which causes the Universe's expansion to accelerate. What is meant by this is that at the current time $ddot{a}(t) > 0$ where $ddot{a}(t)$ is the second derivative of the scale factor with respect to time.

The first way we could look at your question is we could ask whether galaxies currently at at a distance $D_0$ are receding faster than galaxies that were previously at the same distance were in the past when they were at that distance. From the definition of accelerating expansion and the Hubble parameter we can see that accelerating expansion does not imply that the answer to this question is "yes" and in fact if we assume dark energy takes the form of a cosmological constant, ignoring cosmic inflation and we delve into the dynamics of the Universe with find that galaxies currently at $D_0$ must be receding from us slower than the galaxies that were previously at $D_0$ were receding when they were at $D_0$. So in this particular sense the Universe's expansion is slowing down, even though we usually describe it as accelerated.

The second way we could answer your question is to ask whether the recessional velocity of any given galaxy is larger now than it has ever been in the past. The answer to this question is more difficult as accelerated expansion does imply that the recessional velocity of a given galaxy increase with time, but the Universe's rate of expansion in previous epochs was decelerating. However, again taking dark energy as taking the form of a cosmological constant, we see that the answer is that galaxies achieve their highest recessional velocities twice: firstly at the big bang and secondly in the infinite future. So the answer to this question is that galaxies are not currently receding from us faster than they have been at all previous times.

Recession velocity is different from peculiar velocity (i.e. the local velocity wrt to the CMB). We could add the two to find the 'real velocity', but as I've noted recession velocity doesn't have a direct physical meaning so what this 'real velocity' actually means is not straightforward.

Expansion is homogeneous, whereas the vacuum around a black hole is not homogeneous, so in this sense the 'sucking' of a black hole is not the opposite of expansion.