What does it mean to cant or set a blade, and should I file the nicks and burrs off mine?
Cant is a small bend put into the tang, the thin rod at the back of the blade that runs through the grip, so the blade points where your forearm points when your wrist is relaxed. Hold a grip naturally and it sits across the crease of your palm at an angle, which tips a perfectly straight blade up and outward. Canting it down and inward (to the left for a right-hander) lines the point back up with the target, so you can extend without bending your wrist. Sabre blades get canted too, usually forward and slightly in. How much is personal taste, and normal cants pass equipment check easily.
Set gets used loosely. Some fencers mean the same tang bend; others mean a gentle downward curve along a foil or épée blade itself. FIE rules allow that curve only if it is uniform, in the vertical plane, near the middle of the blade and less than 1 cm, while a sabre blade's curve must stay under 4 cm. A blade that has taken a set has simply bent and stayed bent. Beginners do not need to adjust any of this: most complete weapons arrive with a sensible cant, and an armorer can tweak yours quickly. If you do it yourself, bend the tang near the blade's shoulder a little at a time, because stiff blades can snap there.
Yes, smoothing burrs is good practice, done lightly. Blade-on-blade contact raises sharp little slivers along the edges, and they snag uniforms, slice gloves and fingers, and give cracks a place to start. The rules back this up: foil edges must be smoothed so they cannot cut, and épée blades must have no cutting edges. Run a fine file or fine sandpaper along the length of the edge until the raised sliver is flush, then stop. The same rules forbid grinding, filing or heating a blade to alter it, so the job is removing the burr only, never reshaping the blade or thinning it around a nick.
Some damage is past fixing. Retire the blade if a nick is deep enough that smoothing it would mean taking away real metal, if you can see a crack line across the blade, if it keeps kinking in the same spot, or if rust has pitted into a notch. Blades tend to break where they are already damaged, and a snapped blade leaves a jagged end. On an electric foil or épée, a nick near the groove can also cut the wire. When in doubt, show the blade to your club armorer, which takes them a few seconds and costs you nothing.