Can any debtor (credit company/bank) find your new checking/savings account numbers (new banking facility)? Also I am on my mothers checking account and my sons checking account, can a debt collector freeze those accounts or only if only my name is on it?

They can't freeze anything, have no control, unless they have a judgment against you and that is when you have gone to court. Have you gone to court from a summons from a debit collector ? Banks have your SIN #, that's how they trace bank accounts.

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Banks run a special report and often a credit report when you open a bank account so it is easy to find when you open a new one ( or at least apply)

If they get a judgement against you, they may freeze any account you are a owner or joint owner of