The answer should be shown on the electrical appliance itself, often near where the cord enters, or near the main switch. If not, you can find it in the owner's manual. Different mowers have differently sized motors and other features that will determine the minimum amperage necessary.
Note that the longer cord you use, the larger the wires must be, as otherwise it will lose voltage due to the resistance and your lawnmower could be damaged by operating at the lower voltage.
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Usually 30 amp
You can replace a higher rating fuse with a lower rating provided it works with the device without constantly blowing. So try the 30 amp fuse in your lawnmower and if it doesn't blow and the mower works okay, you are fine. If it blows you will have to go back to 40.
You will need AWG #3 if it is a short run.
Depends on the size of the circuit which you did not list.
Either #3 Copper or #2/0 Aluminum.