Do I report self employment income, professional fees as amount invoiced in the tax year, or amount paid to/received by me in the tax year

You would report income in the tax year you earn it, no matter when you receive it.

That depends on the type of your self-employment income. As per the Canada Revenue Agency (CRA), farmers, fishers and self-employed commission agents can use either the cash method or the accrual method to report income. All other self-employment income must be reported using the accrual method. 

When using the cash method, you must report income in the fiscal period you receive it, and deduct expenses in the fiscal year you pay them. When using the accrual method, you must report income in the fiscal period you earn it whether received or not, and deduct expenses in the fiscal period you incur them whether paid or not.

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