We currently (March 2018) do not have explicit rate limits on the number of downlink messages an application can publish on MQTT, we may silently drop messages if it’s too much. Rate limits will be formalized in our v3 infrastructure. Expect limits that “make sense” for LoRaWAN.
Connecting multiple clients will just duplicate what you receive (that’s how MQTT works). Also here we currently (March 2018) don’t limit how many clients can be subscribed to the same application. We hope to support shared subscriptions (where messages are splitted across clients) in the future, but don’t expect that any time soon. Until then, a single MQTT connection per application with a wildcard subscription to all devices in the application is the most efficient in terms of resources.