Are there complete TVS topologies for which $\mathcal{M}(X)\otimes \mathcal{M}(Y)$ is dense in $\mathcal{M}(X\times Y)$

This question is strongly linked to

is the space of all borel measures on $\mathbb{R}^n$ isomorphic to the tensor ... where my answer was (too) quickly accepted and turned out to be more a plan than a a satisfying answer.

Let me elaborate a bit, let $X,Y$ be two locally compact spaces

We consider the corresponding spaces of measures $\mathcal{M}(X),\mathcal{M}(Y),\mathcal{M}(X\times Y)$ and the canonical map $$ can : \mathcal{M}(X)\otimes \mathcal{M}(Y)\rightarrow \mathcal{M}(X\times Y) $$ defined by $$ can(\mu\otimes\nu)(f\otimes g)=\mu(f)\nu(g) $$

As I am not an expert in measure theory (and after having searched and discussed a bit), I ask the following questions whose clarification might be enlighting to read.

Q1) Is $can$ always into ? (generalization/discussion for measurable spaces ?)

Q2) For which complete TVS topology on $\mathcal{M}(X\times Y)$ is the image of $can$ dense in $\mathcal{M}(X\times Y)$ ? (well-known or hand-made answers are accepted).

Q3) Same questions for bounded measures as $$ can(\mathcal{M}^{1}(X)\otimes \mathcal{M}^{1}(Y))\subset \mathcal{M}^{1}(X\times Y) $$

Please give references and/or proofs.