Yes-ish. There are two reasons we are living inside an event horizon. First the accelerating expansion of the universe means that light emitted from earth now will never reach most of the observable universe. We can look up and see galaxies that are already beyond our cone of influence. That is the primary effect. But a secondary effect is that the mass of the universe (Big Bang remains) is sufficient even though not dense as to bend light emitted from it back onto a closed trajectory. So if there is any void beyond the cosmos that we see , observers in that void would see us—our entire observable universe—as a black hole.
No, respectfully, not unless you radically redefine what you mean by "black hole".
If by "black hole" you mean an object sourcing a Kerr-Newman-like metric, then you have the problem that the distribution of matter in the distribution we see is not at all like the interior region of such a metric. The metric one can infer from the bulk distribution of the visible matter is best described by a Robertson-Walker metric.
Under time-reversal, galaxies in R-W fall through each observer-centric horizon, break up into dust and gas that in turn combines into denser higher-energy and lower-entropy states.
While this might seem a little like a "white hole" (defined as a time-reversed BH), since under time-reversal a stellar BH has Hawking radiation rush into its vicinity becoming relatively dense at the time of the bust-up of the BH horizon, the difference is on the other side of that point a much lower entropy neutron star or similar body emerges from the high-entropy BH. Even stepping back a bit, macroscopically, galaxies are a lot more structured than either Hawking radiation; nor is Hawking radiation more structured than the cold relic fields crossing into optical detectability of an observer in time-reversed RW or time-reversed asymptotic de Sitter space.
This is important: the densest phase of a universe like ours is (extremely) low entropy, while the densest phase of the black hole is (extremely) high entropy, especially if we measure just at their respective horizons. Entropy here is Boltzmannian: the log relationship between the observed macrostates and microstates that can produce them. (We could even test this directly by comparing the structures in the relic fields with Hawking radiation if we were to find sufficiently low-mass astrophysical black holes; we can however get some details from the ringing modes of BH mergers).
Additionally, we can consider curvature. The extremely low bound on our universe's Weyl curvature allowed by indirect and direct gravitational wave observations (so far) completely precludes a Kerr-Newman-like solution, where Weyl curvature will be very large. Our imaging of ever older galaxies does not reveal them to be spaghettified.
Finally, it's worth noting that while Kerr-Newman and Robertson-Walker can have optical horizons so can many other solutions. For example, there are optical horizons in the Gödel solution but we obviously aren't in a Gödel universe. There are also many solutions which cannot have optical horizons; a torus or Klein bottle universe is clearly different from a Euclidean one, although all of those can be everywhere flat and horizon-free. So I don't think one should promote the presence of optical horizons into the defining characteristic of a metric.
