Yes, I would call them "jumper hoses". Pull one of your hoses off for connection identification and take it to the shop and describe what you want them to make.
I looked at ebay, and did not see a CD version of either the operator's manual, or repair manual. To learn the routine maintenance procedures for your tractor, get an operator's manual. For repair issues, get a shop/service manual. Ebay usually has a good selection of manuals, as well as Tractor Supply Stores, and internet suppliers.
Yes, your tractor has glow plugs. In the middle of the spring-loaded keyswitch position is the glow plug preheat position. There should be an indicator light to show you are heating the glow plugs. Hold 10-15 seconds and see how it starts. Longer as necessary. Also depends on how cold it is. Your operator's manual will cover this with you as well as many other items.
These are Shibaura (Japan) built tractors, that have a reputation for being ornery cold starters that run rough for a bit after starting. Good tractors otherwise, run fine after getting warmed up.
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Regarding removal of your backhoe, I copied a note from John_Bud regarding removal of a 4500 backhoe. Yours should be similar:
Basically, lay down a sheet of plywood under the hoe. Extend the dipper stick out about 1/2 way, curl the bucket all the way and lower the boom until the pressure is off. Lower the stabilizers. Now loosen the connecting hardware. Should be 2 nuts that are about 1 1/4" to 1 1/2". Somewhere in that range. I actually have different ones on each side -- stuff happens over 45 years....
Then pull the connecting hardware up and back out of the way. It will be sort of stiff unless you have done it recently. With it out of the way (the hoe won't jump off), slowly raise the hoe by pressing down with the stabilizers. Raise it up (and straight by manipulating the dipper stick) until it is free of the saddles (bottom connection point). I like to put 3 or 4 strong jack stands under the hoe box on top of the plywood. 2 in the back and 1 or 2 in the front. Then lower the box down onto the stands, but still at least 2" clear of the saddles to allow for settling. The shut off the engine, take off the hoses, loop the hoses. The smaller one goes on the TRACTOR SIDE and the larger lower pressure return hose is looped on the hoe side. Then just drive off.
Hopefully, you are on a dead flat area. If not, situate it so you drive off slightly uphill. That will make reattachment easier. The trick on it is to get close and use the hoe hydraulics to move the last couple inches. Hopefully you have enough hose to do that. (I don't and it's a PITA).
