What is the capacity of LoRa gateway? How many nodes can be connected to a single gateway?
Capacity is, first and foremost, a consequence of the number of packets that can be received in a given time. A single SX1301 with8 channels can receive approximately 1.5 million packets per day using LoRaWAN protocol.
So, if your application sends one packet per hour, then a single SX1301 gateway can handle about 62,500 end devices.
The capacity of everyday gateways built on a single SPI-connected SX130x chip should be roughy comparable unless there are limitations in a particular design.
For example, poor RF design, noisy power supplies, a high latency SPI-to-USB chip, or an unreliable backend connection could all reduce performance.
Going the other way, gateways with multiple sx130x chips and diplexors could in theory have higher capacity, but only on networks design to make use of that, which (at least in the multi-chip case) TTN is not.
In terms of specifics, for the somewhat unique TTIG there are quite a few threads here which you should carefully review before deciding if you want to go down that route, vs. a more conventional solution.