What is the best known result concerning the existence of companion forms for classical modular forms? Gross' tameness criterion paper is always mentioned with a "unchecked compatibility" caveat? Are the results in this paper bonafide theorems? The ColemanVoloch paper on the topic (which does not rely on these unchecked compatibilities) seems not to allow k=2 (but Gross' paper is fine with k=2). Does KhareWinterberger's proof of Serre's conjecture trump all of this? If so, is Serre's conjecture known unconditionally now or are there still unresolved cases?

It might all depend on precisely what you mean by Serre's conjecture. Various versions are in print. Serre's original conjecture stayed away from $k=1$ and KW resolved this version of the conjecture completely I believe, including all companion forms issues. Did you take a look at the KW papers? They surely give a precise statement of what they prove. Edixhoven made the most optimistic conjecture, allowing weight 1, and I might be wrong but at the back of my mind I suspect that in some cases where the mod $p$ representation is trivial on a decomposition group at $p$, KW only produce a weight $p$ form whereas what is conjectured is that there's a mod $p$ weight 1 form (in the sense of Katz). 


There is also a paper of Toby Gee which, as in KW, uses tools of modularity lifting theorems. He proves the existence of a weight p form as mentioned by Kevin which works as well for Hilbert modular forms. You can check the arxiv paper http://arxiv.org/abs/math/0507507 


In addition to what Kevin already said, there is some work of Bryden Cais and of Gabor Wiese that have removed some and perhaps all of the additional hypotheses. I can't guarantee for sure that it's all done, you should ask them. See http://arxiv.org/abs/1102.2302 and http://www.math.wisc.edu/~cais/Papers/PhDThesis/PhD.html 

