Mortgage solution
The rate does not move for the term, and neither does the payment. What is left to look at is what it costs to leave before the end.

The rate is locked for the whole term (one, two, three or five years most often), and the payment is the same from the first instalment to the last. Whatever the market does in between does not touch your contract. It is the structure to choose when the budget has to be predictable, or when a higher payment would be hard to absorb.
Breaking a fixed rate before maturity costs the greater of two amounts: three months’ interest, or the interest rate differential (IRD), the gap between your rate and the rate the lender could place the money at today, applied to the balance and the time remaining. When rates have fallen since you signed, the IRD can run to several thousand dollars. And it is calculated differently from one lender to the next: several large banks base it on their posted rate, which inflates the bill compared with a lender that uses its actual rate.
A five-year fixed shields you from the market, but it commits you for five years. If you might sell, move or refinance before maturity, the penalty belongs in the calculation from day one. Portability (moving the mortgage to another property), and prepayment privileges, often 10 to 20% of the balance per year, decide how much flexibility you keep despite the locked rate.
At the same rate, two offers can differ by thousands on the penalty alone. Before signing: the IRD method, the percentage you can prepay each year without charge, whether you can increase the payment, and what happens if you move the mortgage. The current market rates are on the mortgage rates page.
Documents to gather
No. Two offers at the same rate can differ by thousands if you need to break the term. The penalty method, the prepayment allowed and portability weigh as much as the rate itself.
Not without breaking the contract: a fixed rate is broken, with the penalty that comes with it. The other direction (variable to fixed), is usually allowed without penalty with the same lender.
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Buying, renewing, refinancing or an unusual situation: describe where you are at, even if it is still vague. Mathieu replies with the next steps and the documents to gather.