Is Knapsack Feasibility and Knapsack with Unit Values NP-Hard?
Just finding a feasible solution is in $P$.  The empty set is a feasible solution.  It achieves an objective of zero.  So, the answer to "does a feasible solution exist?" is always "yes!" (to the extent that the question is even well-defined).  Similarly, the answer to "is any solution whose value is $\ge 0$?" is always "yes!".  Thus, those problems are not NP-hard.

When all values are one, there is also a trivial polynomial-time algorithm to find the optimal solution.  You should be able to find it yourself: just try a few examples, and you will quickly discover the trick.