`Twas brillig, and the slithy toves
Did gyre and gimble in the wabe:
All mimsy were the borogoves,
And the mome raths outgrabe.
I think a Mugwump is similar in nature to a borogove, or a mome rath. Rowling draws from different authors, and one of those authors is Lewis Carroll, I'm almost sure of it. In the P/SS chapter with Ollivander, he keeps saying "Curious... curious...", bringing to mind Alice's reaction to Wonderland and the Looking Glass land. She's obviously made up her own words (Muggle, before it appeared in P/SS, was a non-word). She has her own definitions of what her words mean, and I think Mugwump is one of them. But, while she'll share it if she's asked, she usually doesn't go into detail about what these words mean, and to drive yourself crazy trying to figure out what a Mugwump is is silly, since there's no definition of it outside of J.K. Rowling's head.
About the magid thing... never heard of it. It's highly possible there's not one.