The reacting model would gain LoF only when the Moving model entered base contact and you cannot declare a BS attack unless you have LoF or when in base contact with an enemy.
Yes, you can use a pistol but that's because the pistol has the CC trait allowing it to be used as a close combat weapon. If a model declares a CC attack with a pistol it actually uses its CC attribute instead of BS.
See pg. 33 BS Attack requirements, pg. 41 "Interacting with a CC" and pg. 52 "CC Attack"
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