Can I trim the plastic sticking up from edges of my basement wall?
You're mostly right. The plastic is actually to catch wall water. But, if the wall is solid &amp; tight to the floor, you'd be fine in trimming it, not removing it. If there are any weep holes behind the plastic, you need to keep those trimmed to their height &amp; double their width so any weeping doesn't find it's way onto the floor.

If the wall's not tight to the floor &amp; especially looks like a fairly even gap, then that needs to stay plastic covered as well. Use scissors though instead of a utility knife so you can't accidentally remove it. Since, you still need to leave about 1/4" above the tight floor to wall seam &amp; above any openings.