Let's analyze each proposition step by step according to the rules and the solution provided:

Proposition A:
- Given: Quadrilateral $ABCD$ satisfies $AB=BC=CD=DA$.
- Conclusion: Quadrilateral $ABCD$ could be a planar quadrilateral, not necessarily a rhombus.
- Reason: A quadrilateral with equal sides can exist in three-dimensional space and not be a perfect planar rhombus due to the spatial arrangement.
- Therefore, proposition $A$ is $\boxed{\text{incorrect}}$.

Proposition B:
- Given: Line $l$ does not intersect plane $\alpha$, and point $A$ is on line $l$.
- Consideration: If $l \cap \alpha = \varnothing$, then logically, $A \notin \alpha$ if $A$ is part of $l$.
- Counterexample: If $l \cap \alpha = A$, then $A$ is both on line $l$ and in plane $\alpha$.
- Therefore, proposition $B$ is $\boxed{\text{incorrect}}$.

Proposition C:
- Given: Lines $l$ and $m$ are skew lines, and line $n$ is parallel to line $l$.
- Conclusion: Line $n$ and line $m$ could be intersecting, skew, or parallel.
- Reason: The relationship between $n$ and $m$ is not definitively determined by $n$ being parallel to $l$.
- Therefore, proposition $C$ is $\boxed{\text{incorrect}}$.

Proposition D:
- Given: $m \subset \alpha$, $n \subset \alpha$, $A \in m$, $B \in n$, and both $A$ and $B$ are on line $l$.
- Conclusion: Line $l$ is contained in plane $\alpha$.
- Reason: Since $A$ and $B$ are points in $\alpha$ and also on line $l$, line $l$ must be in plane $\alpha$ to contain both points.
- Therefore, proposition $D$ is $\boxed{\text{correct}}$.

Final Answer:
The incorrect propositions are $A$, $B$, and $C$. Therefore, the final answer is $\boxed{ABC}$.