Hi Liz, I have a TS1610F which is basically the same tractor. It was manufactured sometime in the late 1970's to early 1980's. It certainly can be used to pull a rear mount mower. Be advised that the PTO is not a live PTO. That is, it is driven off the transmission output so that the tractor must be moving forward before the PTO shaft turns. Except that is, if you put the transmission in neutral and let out the clutch it will then turn the mower, but won't do you much good trying to mow without moving forward! Live or independent PTO's will turn full speed all the time independent of ground speed.
The engine oil dipstick on my tractor is on the left side of the engine (sitting in the seat) above the oil pan. It's a cap that screws on. The following are some pics that should help you out to check fluid levels, etc. From left to right: engine oil fill dipstick, hydraulic fluid fill dipstick under seat, transmission oil fill, transmission oil level plug, and fuel injection pump which uses engine oil (fill is the mushroom shaped vent cap on top, level plug is the hex head slotted screw on the lower side). Ask if you have other questions. You should probably get a maintenance manual from a supplier like Len Shaeffer's Town and Country Tractor, who frequents this forum.
Bill