If your status is temporary (visitor, work permit, study permit), your status has a fixed date and you must leave before it expires.
If your status is permanent (i.e. you have PR), divorce will have no affect on your status.
If your child is born in Canada, the child will be a Canadian citizen.
You can marry someone from another country in Canada. All that does is make her your wife, it does nothing to change her status in Canada, and does not give her provincial health insurance.
They can marry while her visitor status is valid, but not after. But, more importantly, if he’s going to sponsor her, the sponsorship application needs to be submitted before her visitor status expires, because he cannot sponsor her after the status expires.
To get married in Canada you’ll need your passport and proof of single status from Saint Lucia.
Once you are married, your wife can sponsor you for permanent residence.
If you marry him in Jamaica and you wish to sponsor him for permanent residence, you can sponsor him immediately after you marry him.
If you want to marry him in Canada, he’ll need a visitor visa to come here, first.
If he’s in Canada already, you can marry him right now.
Once you are married you can sponsor him for permanent residence.
If she is not physically present to get divorced, you have to wait a year before you can divorce her.
You will need your passport and you might need a Statement in Lieu of a Certificate of Non-Impediment to Marriage Abroad, and, if you need that, you’ll need it translated.
Marriage does not guarantee residence. You’ll have to sponsor her for permanent residence once you’re married.
You can legally marry in Canada right now. Once you are married you can look into a spousal visa or spousal sponsorship for Australia. (This is a Canadian site so we cannot give advice about Australia. See this link for sponsoring your spouse.)
Your passport should be enough but contact the Edmonton authorities responsible for issuing marriage licenses to make sure you don’t need proof of single status from Ireland.
