No. Deforestation can happen with clear cutting, farming, or other means. Burning doesn't necessarily lead to deforestation either, as forests can grow back. There are sometimes controlled burns meant to keep large forest fires from occurring.

Trees don't burn well - they're pretty wet inside. This is why you "season' wood for the fireplace. Burning usually takes place after cutting. Forest fires can deforest an area, but where forest fires are natural, the trees mostly just get their bark charred and survive. Many evergreens cannot reseed if the cones aren't opened by fire (heat).

An example of controlled forest burning is in the Sequoia National Park. The actual sequoia's can resist the flames, but their cones with the seeds in it, only open during a forest fire, because all the other plants do die, so the new sapling has plenty of space and sunlight.

Not always, a lot of trees are cut down mechanically, some land is cleared by hand, and sometimes animals grazing can prevent trees growing