Embedded (framed) cobordisms [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? 
 A: The Lie group $SU(2)\cong S^3$, with its left-invariant framing represents a generator of the cobordinsm group of stably-framed 3-manifolds:
$$[(S^3,\text{left-invariant framing})]=\bar 1\in \mathbb Z/24\cong\Omega^\text{fr}_3.$$
If you change the framing on $S^3$, you can reach anything in the set
$$
\{\bar 1,\bar 3, \bar 5, \bar 7,\ldots,\bar {23}\}\subset\mathbb Z/24,
$$
but not the other elements.

Oops!
My answer deals with tangential framings, whereas the question was about normal framings.
I guess I'll leave it here as it might be of independent interest...
A: To Q3. If you ask whether an $M^d$ embedded into $R^n$ bounds a manifold in $R^{n+1}_+$, then here is a partial answer. Let $Emb(d,n)$  denote the cobordism group of embeddings of $d$-dimensional manifolds into $R^n$. Zvagelski has computed that $Emb(3,5) = Z_2$ (See: MR1756714 (2001e:57032) 57R40 57R90)
Take an embedding $f: M^3\to R^5$ representing the non-trivial element of this group. This $M^3$ , like any other $3$-manifold, bounds a $4$-manifold, but that $4$-manifold can not be embedded into $R^6_+$ if the boundary must be mapped by $f.$
