Half the way
The forks should extend at least to the other edge of the pallet that is being lifted. However, a heavier load may need to be farther back, to prevent tipover.
Yes
A forklift mast is the column up which the two blades move up and down to lift and lower a load on a pallet.
You say no, it is not safe.
The height of a pallet is such that a pallet truck or forklift truck can put their blades underneath and lift the pallet. From memory it could be between 6" to 9" high measuring from the ground.
A palette jack is used to relocate a single (usually full) palette. This is not the same as a forklift. It is smaller and can be easily operated. Pallet jacks are use to lift pallets high enough to move the pallet to a different location. They are mainly used for lifting and transporting the pallet.
A pallet lifter is a tool used in the construction industry generally, to lift pallets which may be used to transport goods or equipment. It has the same kind of functionality as forklift forks.
It would be the safest way to move it. It would also be the easiest way.
Manual pallet jacks don't require one. Pallet jacks with electric power (there are also diesel pallet jacks, but they're extremely rare) are licensed by going to a designated individual in your company and asking to be trained and tested, or to a community college that has a forklift certification course.
Various kinds can be used, the most common probably being forklift trucks and pallet trucks.
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