Here's how it works.
First off, the tractor is negative to ground.
Secondly, I'm going to assume that you still have the correct start solenoid in this tractor and not some solenoid designed for a Ford car. They look the same but they are not wired the same internally.
When you turn the keyswitch to the "START" position, juice is supposed to flow to one of the small terminals on the solenoid shown in the photo. It doesn't matter which terminal.
The other small terminal must find ground in order for the solenoid to pull in. This is where the safety switches come in because they interrupt the grounding of the solenoid if the PTO lever is not fully disengaged and the travel lever is not in the "Neutral" position.
In order to determine where the problem is, use a piece of wire to bypass the safety switches temporarily. Put one end of that wire to the negative battery terminal and hook the other end to the small terminal on the solenoid that does NOT go to the ignition switch. Usually, that terminal has a black wire on it.
Try the keyswitch and see if the tractor starts. If it does, then that means everything is OK but you have a safety switch issue. Do yourself and your loved ones a favour and fix the safety switch. They're there for a good reason. Follow that wire down to the PTO safety switch. Make sure that it is attached to the switch. Make sure that the wire on the other side of that switch is attached. That wire goes from there to the neutral switch just under the dash where the travel lever is. You will see two tiny carriage bolt heads on the dash. These are what secure the neutral switch.
There is a short piece of round rod that moves across the neutral switch whenever you move the travel lever. This rod comes in contact with a brass rivet in the center of the neutral switch and provides the needed ground. Sometimes it's a defective switch and sometimes it's just rust, corrosion or too much wear in the travel lever components to make a good ground.
If it does not start with the jumper wire, then the likely problem is the start solenoid. These can be had from the link below. They are "isolated ground" solenoids, not "case grounded" solenoids. Buying one from the link below will ensure that you get the correct type for your tractor.
New neutral switches cost less than thirty bucks and you can order one on-line from the link below. I strongly urge you to use the serial number of your tractor to obtain the correct Operator's Manual and Parts Manual for your tractor because those two books will be invaluable in helping you keep this tractor in good repair. It will be the best thirty bucks you ever spent.
It's anybodies guess as to the hydraulic leak. It could be the front seal on the pump or a loose clamp on the suction line. The best thing to do is to give this tractor a good wash to remove all the dirt, grease and whatever else is covering the parts so that you can trace where the oil is originating from.