Inventors of the South Tigris

No — only dice in Ready, Determined, or Inspired are considered “available” for placing on Camels; Exhausted dice are not usable (see page 14) and the die-state definitions are explained on page 8 (Ready/Determined/Inspired vs Exhausted).

Yes — the Test action begins by placing 1 White Die from the Main Supply onto a Camel (its value doesn't matter), and this must be done first (page 17).

When you pay a Craftsperson you pay the Silver printed on their current Tower Tile, immediately turn that Craftsperson facedown (Inactive) and then raise them up one Tower level if possible; progressing Tower Tiles is resolved when the lowest tile has no Craftspeople (page 9).

Any Die gained to the Study is placed on the bottom Study space for that colour (never higher) and placing a Die there immediately forces you to remove 1 Die (any eligible Die not on a Camel or in a Workshop) back to the supply (page 8).

No — each Craftsperson can only be used once per task, so you cannot use them, refresh them mid-task, and use them again for that same task (page 22).

You must immediately place the Workshop Tile onto your Player Board into the left-most empty space of the chosen row for free; placing it into columns further right costs 1 Silver per column beyond the left-most incomplete column, and you resolve any covered effects immediately (page 10).