Throwing charges at Nordström black hole

Suppose you have a Nordström black hole.

At large distance, both Newton gravitational attraction and Coulomb
repulsion increase with inverse square of distance. Therefore, you can
pick test bodies with suitable mass to charge ratio that the Coulomb
repulsion exactly compensates Newton attraction irrespective of
distance. The charge would not feel the presence of black hole.

What about close to black hole? Does a small test body with like
charge to Nordström black hole still feel infinite attraction at even
horizon and large but finite attraction outside and near the horizon?

What about a Nordström black hole and test bodies such that the
Coulomb repulsion exceeds the Newton attraction for all large
distances? Does the infinite attraction at event horizon still apply?
And would there also be large but finite attraction outside and near
event horizon? As well as large but finite Coulomb repulsion somewhere
outside?

Can you throw charges at Nordström black hole, which are repelled by
Coulomb repulsion but cross the barrier by their kinetic energy and
add to the charge of the hole?

How far can that process go?
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