What is Airbnb's contractual obligation in cases where something is wrong with your booking?

I can’t tell you what they would actually do, but I’m going to quote from the T&C anyway, because that’s what lays out what they’re legally obliged to do. And, alas, the answer is basically nothing. Boldface mine:

The Hosts, not Airbnb, are solely responsible for honoring any
confirmed bookings and making available any Accommodations reserved
through the Site, Application and Services. If you, as a Guest, choose
to enter into a transaction with a Host for the booking of an
Accommodation, you agree and understand that you will be required to
enter into an agreement with the Host and you agree to accept any
terms, conditions, rules and restrictions associated with such
Accommodation imposed by the Host. You acknowledge and agree that you,
and not Airbnb, will be responsible for performing the obligations of
any such agreements, that Airbnb is not a party to such agreements,
and that, with the exception of its payment obligations hereunder,
Airbnb disclaims all liability arising from or related to any such
agreements.

So basically, if the host cancels your booking for any reason (#2), Airbnb will refund your money and suggest other listings nearby:

If a Host cancels a confirmed booking made via the Site, Services, and
Application, (i) Airbnb Payments will refund the Total Fees for such
booking to the applicable Guest within a commercially reasonable time
of the cancellation and (ii) the Guest will receive an email or other
communication from Airbnb containing alternative Listings and other
related information.

If there are no other listings nearby because of the World Cup or a Godzilla rampage, too bad.

More or less the same applies to an apartment you can’t get into (#1) or an unusable/defective apartment (#3), which is covered by a separate but similar Guest Refund Policy. This policy also applies to cancellations made “shortly before the scheduled start of the reservation”, although what exactly this means (hours before? same day?) is left undefined.

If you are a Guest and suffer a Travel Issue, we agree, at our
discretion, to either (i) reimburse you up to the amount paid by you
through the Site, as determined by Airbnb in our discretion, depending
on the nature of the Travel Issue suffered or (ii) use our reasonable
efforts to find and book you another Accommodation for any unused
nights left in your reservation which in our determination is
reasonably comparable to the Accommodation described in your original
reservation in terms of size, rooms, features and quality. All
determinations of Airbnb with respect to the Guest Refund Policy,
including without limitation the size of any refund, shall be final
and binding on the Guests and Hosts.

This seems more generous at first glance, since it looks like they’re promising to
actively find you alternative accommodations including non-Airbnb options, but on more careful reading there’s that “or” in there. In other words, they can take option (i), refund your money and say “too bad”.

Now, that’s the T&C. Their FAQ claims they’d actually go beyond this minimum and offer you automatic credit to upgrade:

What happens if a host cancels my reservation?

3) Book something nicer. We’ll help cover the difference if you want to
book a more expensive listing. Just look for an email from us with
details on how much credit we can offer based on your existing
reservation amount.

Although reports on the net claim that credit is not too generous:

In our case, we spent over €1,200 and they offered €37 worth of a
voucher for the inconvenience. That’s less than 3% of the price paid.

All this looks a bit mean at first glance, but truth be told, if you examine the fine print of most any hotel chain’s T&C, you’ll find pretty much the same wording. Most better hotels do adopt the practice of “comping” your room if they have to turn you away, meaning they’ll find alternative accommodations and foot the bill, but this is customer service, not a requirement — and I’d expect Airbnb to go beyond the minimum as well if you really do run into the worst-case scenario of knocking at somebody’s door in the middle of the night and not getting an answer.