There are some big players that use MQTT although i am not sure about the QoS levels. I know WhatsApp used MQTT, although i am not sure if they still do it not or what QoS they used. My bet would be they used QoS 1.

There are multiple brokers for MQTT: Mosquitto, HiveMQ (Java), VerneMQ (Erlang), EMQ: the one we used (Erlang) etc. You can find out more brokers that are available as well.