There is no one way to do things. Ship design is continually evolving.
In general, cargo ships are low and slow, as in powered by large 2-stroke diesel engines with big propellors and slow speeds. Higher speed vessels use smaller 4-stroke engines with smaller propellors and higher speeds.
Traditionally, propulsion has been diesel, but as ship sizes get larger, companies seek energy efficiency and specialiaty requirements (noise, passenger comfort, etc.), diesel-electric is being embraced (diesel to electrical propulsion).
We have two requirements: propulsion and auxiliary loads. Auxiliary powers everything else. Diesel-drives have diesel propulsion (2 or 4 stroke) and 4-stroke auxiliaries. Diesel-electric drives have 4-stroke gensets (diesel generator) generating AC power and large electric motors for propulsion.
Ships use 50Hz or 60Hz auxiliaries. A rough estimate would be 5% of propulsion power would power auxiliaries. A lot of energy goes up the stack. Heat exchangers recovery this heat to heat boilers, which can be used as required. In principle, this energy could be used to generate the electricity powering some or all of the power for the auxiliaries. The problem being synchronizing this power with 50Hz or 60Hz auxiliary diesel generated power.
Yes to all possibilities.
And this sort of answers this also. As ships get larger and IMO forces energy efficiency on ship owners, diesel-electric ships become the predominant choice.
Again, this would be vessel specific, but most cargo pumps are electrical. Electrically driven pumps are easier to control, but diesel-engine pumps have more capacity, with one cavaet, they burn more fuel.
So FiFi monitors (long distance fire-fighting pumps putting out up to 2 tons/s - FiFi 3 = 9600 m3/hr @ 70m height) are typically main diesel-engine driven pumps. They put out enough water to drive ships backwards over 3 knots. In this case, it makes sense to use large capacity of the propulsion engines.
Cargo pumps are typically electrically driven, so the load can be provided by auxiliaries or even shore power (burn no fuel = cheaper electricity). This is more of an efficiency or scale issue. You can hammer a nail with a sled hammer, but you don't want to be holding the nail.
8-16 electrically driven cargo pumps vs 1 or 2 diesels running at low efficiencies. Diesels have the best fuel consumption around 75% to 85% of MCR (Manufacturers Continuous Rating). Power up auxiliaries and match load on auxiliaries to load required by pumps. Propulsion engines would be below 25% load.