Fixed in supply means the elasticity of supply is zero. No matter price has increased to a very high level, QS of the goods still remains unchanged. Therefore, the supply curve is vertical.
To know the elasticity of supply, we need to look at the change in QS as a result of a change in P. For fixed supply, the change in QS is zero whatever the change in price.
For example, land is fixed in supply. Because QS of land does not change with price. If Hong Kong is 1000 km square, then, without reclamation, the size of Hong Kong is still 1000 km square no matter land price has increaed to sky high level. But if there is reclamation and thus new land, the supply of land will increase. This does not mean the supply will become upward sloping. Instead it is still vertical but it shifts to the right.
This example is similar to your examples given in the question. Supply is fixed but the curve can shift in or out to reflect the change in supply.