As far as the first question is concerned, I can make comments on it.

In the piorineering work by Braverman, it was shown that the intersection cohomology groups $\oplus IH_{T\times (\mathbb{C}^*)^2}({\cal U}_{G,B})$ of the Uhlenbeck compactification ${\cal U}_{G,B}$ of the moduli space $Bun_{G,B}$ of parabolic $G$-bundle have an action of affine Lie algebra $\hat{\mathfrak{g}}^{\vee}$.

http://arxiv.org/abs/math/0401409

This result was translated in physics language by Alday and Tachikawa that the instanton partition function of $SU(2)$ gauge theory with a full surface operator is equal to the conformal blocks of the affine $\hat{\mathfrak{sl}}_2$ algebra.

http://arxiv.org/abs/1005.4469

The extension to $\hat{\mathfrak{sl}}_N$ has been discussed by Wyllard et al.

http://arxiv.org/abs/1008.1412

Therefore, it is expected that the partition function of $\cal{N}=2$ gauge theory on $S^4$ with a full surface operator is equivalent to the correlation function of the $SL(N)$ WZW theory.

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