There are 2 department level settings Mail User Max Load and Chat User Max Load to control maximum email and chat are pushed by system. Setttings work indivdually for chat and email and not together.
For integrated email or chat max concurrent activities can be set at queue level from admin console.
To restrict pull access for some queues, from admin console you can control permission for that user on queues. If pull permission is not given he cannot pull from that queue.