Gear oil leak?

Hi, I have a 250 cc Kart. Its leaking some milky whitish oil and spraying water. The pics attached shows where the leaks are coming from. I don't even know what the parts are called . BUT I CAN LEARN. I just got the Kart and the guy said all it needed was a new carburetor. after changing the carburetor, I put it in gear and it would go forward but grinded to go in reverse. After only going forward a couple feet it popped out of gear and now wont go into either reverse or forward. I left it running to see if I could see anything and noticed some white milky oil flowing from the left little box as circled in red in the picture attached. I checked the oil from the box to the right and cleaned the Sight Glass (BTW the oil was black and thick and the glass was caked on with oil). I found out that its supposed to be gear oil and so i am assuming that is the gear box.. (who knew! Hopefully y'all do because I didn't..... ) Anyway, if that is where the gear oil is and I know where the regular engine oil goes, then why is there milky oil leaking from the little box to the left?
Also, when the gas peddle is pushed, water sprays out from the other circled spot on the pic.
Any help would be great, even if all you can do is identify the names of the different parts on the pic. That way I can search it better.
P.S. Obviously I am no mechanic. I just bought this for my two boys and want to get it running for them. Thank you in advance!

Attachments

Full rear view of problem areas.

magnified view of water leak

magnified view of milky oil leak

Close-up oil leak.png (157.31 KiB) Viewed 609 times

Looks like a blown head gasket and the other is a gearbox seal leaking watered down gear oil