I'm programming chat app with MQTT protocol
You can see here mqtt.org about MQTT
My used broker is mosquito
What struck my mind is that
How many users can connect to Mosquito broker?
I saw 100k in some website but i am not sure
This is dependent on a number of factors:
You also need to configure the broker/OS to get the most out of it, e.g. for mosquitto you need to set the number of open file handles on Linux to the maximum.
For a large scale app you may want to look at one of the brokers that supports federation/clustering to spread the load and allow fail over.