Can a force use naval transport from a port that they occupy, but do not control? Can they use naval transport from a port that they are besieging? If so, does the presence of enemy naval units in the besieged port prohibit a naval move? The rules seem to indicate that the only requirement is that the units occupy a port, but just wanted to confirm.
Yes, yes, no.
The presence of enemy units in the destination port prevents movement, not in the origin.
Do the restrictions on builds when a foreign war is active apply to builds gained via events? Sometimes card says "place", not "build", not sure if this is relevant.
Place, build etc are all considered equivalent language.