NYC Mesh – community-owned network to replace your current internet connection

2 - a service like this doesn't rely on much fiber at all, outside of the point(s) where the mesh connects to the rest of the internet. Its almost all point-to-point wireless, with the points eventually converging back on the base stations at datacenters.

3 - the common term for this kind of facility is a "carrier hotel" or "ix" (like internet exchange). A carrier hotel is usually a dedicated-purpose facility where lots of different providers connect their networks together specifically for that purpose, but, hypothetically even a reasonably well-connected commercial datacenter will have at least a couple of carrier connections on site who could be used to create a mesh network base.

Facebook.

I've lived in 4 apartments in 7 years and never once had a choice.

1. They are likely using point-to-point/point-to-multi-point directional wireless equipment, designed for longer distance high bandwidth wireless connections where you know the fixed location of the transmitters/receivers and can tune/optimize for that purpose. Those devices you mentioned have hardware designed for omnidirectional local WiFi (broadcast & receive everywhere within x,00 feet). You could have one of those in you're home to provide wifi, and a point to point (with a directional antenna device designed for building-to-building/house-to-house connections) on you're roof to connect to the mesh network. Think of it as a mini satellite dish, pointed to the location from which the signal is being transmitted. Also, using standardized equiptment is more practical to efficiently deploy monitor and manager for a project like this.

2. No. The fiber will be there eventually, and wireless bandwidth is by far slowest link in the chain (the theoretical max speed of 802.11ac is eight 160MHz 256-QAM channels, each of which are capable of 866.7Mbps). Cat6 ethernet cable consisting of 8 conducting wires is capable of providing 10,000Mbps (10-Gigabit) maximum data rate, up to ~100m between powered devices. There are several types of fiber, OM4 is capable of 100,000Mbps over distances up to 150m. These are theoretical speeds, IRL divide by 2 twice and that's a good bencmark target (by 5 for WiFi ;-).

3. Internet Exchange Point https://en.m.wikipedia.org/wiki/Internet_exchange_point

Usually you're looking for 'co-los' (co-locations), buildings that host multi-company/parties server and network equipment and have high bandwidth connections to internet backbone provider networks.