Amphibious assaults can be done in two steps, consisting of a sea battle and a land battle. In your example, both the cruiser and the transport would attack the destroyer. If the attackers win, the transport can offload and the land battle will occur. If the transport ends up retreating (or being sunk), the land battle will not occur and the transport may not offload.
Question about damage markers?
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Let’s say a country has only 1 build possible. Meaning, the country in question removes enough damage markers to give it 1 build. Can they build 1 Inf and 1 IC, if the IC is to be placed in another territory? Or, do they need 2 builds?
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He can build 1 IC and 1 INF. The damage markers only indicate the limited production of a damaged IC.
A newly built IC is considered to be build in a new territory, with the resources and manpower available of the country it is in.