uranium from sea water does not take that much energy, it can be selectively absorbed with certain fibers, from which the yellow cake (uranium ore) can be easily extracted. The main energy needed is for the pumps for flowing the water past the fiber. This is not the same extraction method used for hydrogen or many other compounds involving centrifuges, this is a much much cheaper and energy efficient method.
As for the being finite, with scrap you can already get an unlimited supply of most minerals, so that shouldn't be a concern. Stuff from ocean water is supposed to be practically unlimited anyway, just certain things are more difficult to extract.
As for determining if it is ocean water, you could do a check that it is in the right biome, then some sort of check for volume of water (when placing the extractor make sure there are more than a certain number of water blocks connected to the one it is extractring from, then have it only be able to use water it collects, not any other source of water)*. This way the only way to cheat it would be to build a giant artifical pond in an ocean biome, ie a waste of time.
*you could have it run a check on the block next to the water block it is placed in, make sure it is water, then check one next to that, and repeat for some large number. only if it is enough water will it allow the extractor to be placed at all.
The simplest way would be to ignore any of the above checks, and just have a biome restriction to ocean and beach biomes. and have the extractor not accept any other input besides the water surrounding it.
A possible mechanic for making the extractor more limited, would be to have it consume an extraction fiber, where different fibers can extract either specific or a range of specific materials, and take different times to do so. Then to make it more bulky you can have it require some large number of filled fibers to create a single piece of ore. also limiting the stack size of the unfilled fibers would then require a system to provide the extractor with fibers and remove the fibers when done. This would make it a bit more difficult to just have one machine that makes everything, like a high speed recycler turning cobble into anything you need.