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If Hawking radiation comes from outside the event horizon, how will it make the black hole evaporate? Also, how can the radiation be related to a blackhole's mass if it's coming from somewhere outside the black hole / outside its event horizon?

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If Hawking radiation comes from outside the event horizon, how will it make the black hole evaporate?

The gravitational field of the black hole extends outside its horizon, that is how it keeps attracting matter and how matter exists in the horizon, the radius of complete absorption by the black hole. An explanation can be found here, partial quote:

the dry facts are that two real particles (e.g., two photons, or an electron and a positron) are created from the energy in the very strong gravitational field near the horizon of the black hole - from a classical external gravitational field (if gravitation is treated classically), or possibly from two gravitons (in effective quantum gravity at lone loop), not from the vacuum.

italics mine.

Also, how can the radiation be related to a blackhole's mass if it's coming from somewhere outside the black hole / outside its event horizon?

The energy is provided by the black hole's mass through the gravitational field, and the strength of the gravitational field depends on the mass.

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