A 112 Natural 20 only.
An improvised weapon scores a threat on a natural roll of 20 and deals double damage on a critical hit.
A 113 Ask your DM.
To determine the size category and appropriate damage for an improvised weapon, compare its relative size and damage potential to the weapon list to find a reasonable match.
The "appropriate damage" for an improvised weapon includes the amount of damage and the type of damage. The rules already specify the amount, but it's up to the DM to determine the type. Practically speaking, an arrow is only suitable for piercing damage (since it would break easily when striking with any lateral force), so that's the way most DMs would call it.

A 114 Ask your DM.

Bolts for light and heavy crossbows have the same cost and weight, but that's not the same as saying they're the same size. The answer depends on whether the difference of a heavy crossbow compared to a light crossbow is in a longer pull or just stouter construction, in addition to the loading mechanics. The rules don't have this level of detail, so it's up to the individual DM whether the bolts are interchangeable.