H2 console doesn’t let you to work with the whole cluster. The cluster consists of many nodes each of which has its own instance of H2 engine running. H2 console connects to a particular H2 server running on a concrete node and will operate over the dataset that is stored on the node only.
To execute SQL queries over Ignite cluster you should use GridGain Web Console
No, this is impossible. Also keep in mind, that H2 debug console runs queries locally without any distributive capabilities. To do the same you can send closures to your cluster nodes and run local SQL queries.
But may be it is a good idea to be able to start the console on all the nodes. This may be useful for development environment.