I don't know about "web" scale, but it will definitely scale horizontally without using any external tools/extensions.

There's still a somewhat annoying limitation that is related to the status of table partitioning in postgresql.

In fact the planner automatically choose the right child table, be it on the same db or into another server, for UPDATE and SELECT statements but not for INSERTs. This is a known limitation and there's active work to fix it but don't hold your breath though.

Yes, unlike 99% of the start-ups who demand it.

No, you will still need to plan your dynamic loading intelligently.