Model #s may help. Maybe it is missing it's top.

I,m not sure what the mod # is the only #,s I can find on it don,t match any mod #,s I find on the internet but thesd are the #,s Ifound Tecumesh-peerless6733-p1 (r) on the case then it has a bar code#30860062 (r)6845-p91 then on the trans axle it has peerless 2000-0028 silent-?

Puking oil out the atmospheric vent on a hydrostat can mean a few different things (or related things).
(1) The oil has been in service too long and has degraded to the point that the anti-foaming additives in the oil are no longer effective.
(2) The transmission is overheating. This might be caused by a layer of insulating grass and debris that has accumulated on the top surfaces of the tranny over time.
A damaged, or "grass clogged" fan (rare occurance) would do this too.
A common practice by operators of a hydrostatic drive tractor which results in overheating the hydro is running the engine RPMs too slow. A hydrostat sheds heat because the fan blows cooling air over the top sufaces of the tranny case. The fan in mounted to the tranny input pulley and only turns as fast as the input pulley. If you run the engine at low RPM, the fan is turning slow and will not wash enough cooling air over the tranny to remove the heat, but the tranny still develops as much (or more) heat at low RPM as when the RPMs are high.
The proper way to operate a hydrostatic drive tranny is to run the engine at max governed RPM and control your ground speed by using the transmission control lever, or foot pedal, whichever is featured.
If you are already operating the engine at max RPM, and there is nothing wrong with the fan, and the trans case is clean.............you need to change the oil in the tranny.