1. Get the application for non-residency and read it thoroughly
2. You can own a house if (a) it is rented to a non-related third party and (b) the lease is yearly with at least a 3 month notice to vacate period before the expiry date of the lease
3. You can have a bank account so long as it is there for a purpose i.e. to deposit the rent cheques in and to move money for maintenance on the house.
4. Perhaps CRA can't check your earnings overseas directly, however, it is on YOU the tax payer to PROVE that the amount of money you declare IS the amount of money you earned. It is not CRA's problem to prove that you earned more or less.
5. If you are getting housing, tickets, medical, children's education allowance etc. etc. etc. These are considered taxable benefits by CRA and MUST be reported as income on your tax return.
6. Even if you don't file a return voluntarily, CRA can request and require you to do so - failure to do is an offence and you can be charged accordingly with fines and other penalties including jail (if they determine you are evading tax payments).

Get yourself the forms and information from online then contact a good tax accountant - not a lawyer - who has experience in these matters. It's not difficult to get non-residency status, just follow the rules.
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