Lots for fossils are taken our of the river bed and kept and I have not heard of any one arrested . I think you may be referring to Corps of engineer Lakes
Its a public river, and to my knowledge fossils arent protected. So have at it.
Yes
You can keep them. Be sure and take drinks and snacks with you as there is nothing available there. Also a plastic bag for muddy/wet clothes helps.
Finders keepers.
I don't know what public law you refer to but I believe you can keep any fossils you find there.
Thanks! Your answer is awaiting moderation.