The piles of soil in your lawn are brought to you by a star nosed mole.  They leave a mound of dirt as a sign of their presence when . Their favorite foods are earthworms and insect larvae. Star nosed moles tunnel deeper than eastern moles so trapping is not as effective for control. MSU recommends poison bait shaped like earthworms.
More info in the attached links:
Moles in the Lawn-MSU
https://extension.psu.edu/moles
https://blogs.cornell.edu/nysipm/2020/10/14/dealing-with-mole-problems-in-turfgrass/
https://www.canr.msu.edu/uploads/files/moles.pdf
Controlling Moles, Racoons & Skunks - MSU
How to Control Moles-SG-MSU - a bait recommendation
Wear latex gloves when setting the trap or placing the bait to keep human scent off the trap or bait. Follow the instructions on the package. To win this battle you must be patient and persistent. Start now! MSU Extension does not endorse any retailers or brands. Good luck!
Your 3rd photo (of scat) isn't clear enough for me to identify who left it, so I found links to articles on scat identification that may help you figure it out:
https://lancaster.unl.edu/hort/mastergardener/resources/Wildlife-Scat%20ID%20KEY.pdf
https://drive.google.com/file/d/1shPvwoW5gYnnElwCActrJMbRk5oKgg9I/view
http://www.biokids.umich.edu/guides/tracks_and_sign/leavebehind/scat/
https://www.canr.msu.edu/news/habitat_in_the_backyard_part_6_poop