I have 2 questions. (1) Is the starter wire connected directly to the solenoid? I can't follow the wire because it goes through the frame and I may have to rewire the solenoid because the replacement solenoid terminals are smaller than the original.
(2) I can jump start the tractor with a screw driver across the solenoid terminals and it starts immediately. Does this mean the solenoid is bad or is it the ignition switch? I don't know how to use a multimeter (I have one though) so checking the voltage and resistance is of no help to me.

Thanks in advance,

Hi,
Shorting across the terminals and starting means the battery, starter and engine are functioning. Must put things in context, those are the things in use when you do that.
I cannot answer beyond that with ease, though I can try to step you through the use of your VOM (I was certified in electronics over 20 years ago.)
Peace,
Clarke

Is the starter directly wired to the solenoid?

Hi,
I merged your first and second posts; since I replied to the first, I get an automatic email if you add to it. Do not otherwise.
Yes, the battery + terminal attaches to one of the large solenoid terminals and the starter is attached to the other. Your solenoid has two other smaller terminals; one is a ground and the other is the positive trigger. Safety switches can connect through either of the circuits. Interrupting either will cause the solenoid not to function normally. At fault could be the solenoid, one or more safety switches or the ignition switch.
Peace,
Clarke