No, it is not a lawful way to make council decisions. The chairman has few rights beyond those of an ordinary councillor and certainly has no right to demand that councillors respond to his emails, with or without a deadline.
A council decision can only be made at a properly constituted meeting, based on agenda items that were published three clear days ahead of the meeting, and the meeting must be open to the public (except when the public is specifically excluded for particular reasons). Only the councillors present at the meeting can be involved in decisions.
Decisions can be delegated to the clerk, but this is normally done on specific matters or subject to specific guidelines.
It is not possible to make lawful decisions as a result of email or any other kind of correspondence.