Nope, no need to stain. I actually haven't really looked at seawater much to be honest, but you're definitely going to get a different set of lifeforms in seawater than you will from fresh pond water. Making comparisons between them might be a good thing to record in your notebook, which is a great idea btw. In the sea water you might see some tiny crustaceans like copepods but not likely to see rotifers for example. Could see tardigrades in either, though!
In either case, pond or sea, you shouldn't need to worry about staining anything. Most of these things have their own pigmentation, especially diatoms. The critters will tend to look semi-transparent or transparent but with very distinct edges, something like this so no, no need to stain. In fact you shouldn't stain anyway because it will likely kill the creatures in your sample so you won't see their activity.
As for the terrariums, awesome. There is a lot to be considered there, but what an amazing way to truly delve into those questions. If or when you do set something like that up, I hope you post about it here. I'd love to read about your findings.
This looks like the kind of unrestrained, unsophisticated blatant anti-Jew propaganda of 1930s Germany or anti-black propaganda of post civil war United States that everyone since that time, especially liberals, like to pretend they would never have fallen for. So crass, so absurd, so obvious. But when some chud or gammon mulches their brainworm manure through an AI slop machine, suddenly an image that even the most frothing Nazi who died in 1945 would have found to be a little too on-the-nose is seen as an interesting artistic political perspective. Makes me fucking nauseous.