It is an Anubias, possibly coffiefolia, and is not a floater. It can be attached to a piece of wood or stone or planted in the substrate. The rhizome must be completely above the substrate if planted. Only the roots go into the substrate. It will thrive in low light conditions. you can leave the damaged leaves for now and remove if they get worse.
You could cut the rhizome to make several pieces if you like.
With Anubias, I usually soak the leaves (right to the rhizome) in a 1:20 bleach/water solution for a minute or two, to kill any algae.
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