Mine did the same thing and I tried to scrub them off, then my sister who is great with plants told me they were BABIES! Sure enough, the ones I didn't scrub off turned in to new java fern plants! Let them grow a bit (they will develop leaves and roots) and then gently pull them off and plant them. Congrats!
You don't have to plant it. U just rinse it off and put it in water. Just let it float.
Not really because these plants go in the water. If algae is your problem then sunlight is more than likely your enemy. You could try some floating plants like Java moss. But I’m not sure it will fix the problem entirely if it is an outdoor fountain
Koi are terrible to plants. If you want the investment worth it, I’d recommend switching to silk artificial plants. They look very natural and can increase bio load which is beneficial for koi. If you don’t mind the plant being destroyed then it should be fine.