Sounds like Sunny’s English and their ilk are up to their old antics as usual! First, tell them that no genuine hard-copy of the contract in your hand means no contract at all. Goodbye! No month-notice, no discussion. Goodbye.
Like Deven asked, what visa are you on? If you’ve already got a work permit (highly unlikely) then things will be difficult when trying to get a new job. Plus, you will be linked through the school to the PSB and the school could probably report you on it.
Tourist or Student visa would mean that you’re not even “legal” to work anyways and are free to walk away and find something else.