[The title initially was "Actions of gauge groups on framed cobordisms. This has been changed.]

This question is a follow-up to my answer to When is a submanifold of $\mathbf R^n$ given by global equations?

Suppose $M$ is a smooth compact $d$-dimensional submanifold of $\mathbb{R}^n$ given as the transversal zero locus of $k=n-d$ functions. The normal bundle of $M$ in $\mathbb{R}^n$ is framed and moreover, it turns out that $M$ is ~~framed cobordant to 0~~ bounds a submanifold of $\mathbb{R}^n$, unless $d=0$. (At first I thought this was a consequence of Sard's lemma; now I think this is not quite so obvious but true nonetheless.)

Q1. I would like to ask: is there a submanifold $M$ of $\mathbb{R}^n$ with trivial normal bundle such that no framing of this bundle makes $M$ framed cobordant to 0? ~~A positive answer to this would mean that the answer to the above-mentioned question is negative.~~ [This question still stands, but I don't think it is directly related to the above mentioned question in the other thread.]

Q2. Is there a manifold $M\subset\mathbb{R}^n$ with trivial normal bundle such that no $N$ with boundary $M$ can be embedded in $\mathbb{R}^n$? Presumably this is more difficult than Q1. [But if the answer is positive, this would mean that there are submanifolds of $\mathbb{R}^n$ with trivial normal bundles that can't be given by global equations.]

In general, if $M$ is embeddable in $\mathbb{R}^n$, there seems to be no reason any of the manifolds bounded by $M$ should be. However I do not know of any obstructions or counter-examples.

Q3. What if we drop the condition that the normal bundle is trivial in Q2 and replace it with the weaker condition that $M$ is cobordant to 0, i.e., that all Stiefel-Whitney numbers of $M$ are 0?