Although I've done a lot of organometallic chemistry, I can't say I've ever done anything like this.
The first equation looks correct except there's no water on the right (except the "(aq)" -- I'm not sure that's correct), but I'm pretty sure you understand that. You are driving off water so I'd put it on the right and remove the "(aq)".
Manganese usually forms Manganese (II) compounds. Depending on how hot it got, it is probably MnO (loses 1 more mole of water).
It's probably a stepwise process. First heating to drive off ethanol and form Manganese (II) hydroxide, then strong heating to drive off more water, and form MnO, and also decompose any additional organic material in the residue.
I am puzzled. Acetone formation from Ethanoate requires oxidation. That implies some reduction process. Are you forming manganese metal? Probably not. Maybe it's a disproportionation reaction of the organic, itself. You must be forming carbon (I guess it does turn black, as you mentioneed.) The reduction of carbon supports the oxidation of ethanoate (ethanol) to acetone.