For 3 and 4, you will NOT collect your checked bag at connection point (MUC).

You enter Schengen at MUC but your bag goes through custom (which oftentimes means simply putting your bag on a X-ray and that's it) technically enters Schengen at FRA.

I have been on similar itin. (UA to Germany and LH to somewhere) but mostly through FRA. Shouldn't be different