barb,
Welcome to the Forum! The PTO is the "Power Take Off" unit. It is what turns on when you flip the "PTO" switch, and engages the blades. A low battery, or bad charging circuit may cause the PTO not to turn on.
Best way to check the charging circuit is to measure the voltage at the battery when the tractor is running at full speed with a digital voltmeter. It should be between 13.4-14volts. If the voltage is less than that, the PTO won't be able to turn on. Other causes are the switch itself sometimes goes bad.
Any standard lawn tractor battery from your favorite lawn & garden store will do, nothing special there.
The plugs are harder to find, and you may have to order them online. They are NGK brand, type BPR5HS
Rattosh51
YT6800