[QLDs4]

So is it imperative I get that washer doohickey thing (probably right?

If the sprocket moves side to side along the shaft it MIGHT chew up the sprocket cover, chain guide and swing arm. If the bolts are too long they will chew the engine casting, just get them long enough that they don't come out the back of the sprocket by more than a couple of mm.

Ive seen some laser realigning tool

You have marks on the swingarm and the plates that the axle goes through. Use the marks to align the wheel.

So today I received my front sprocket and rear sprocket, but still no chain, now how bad would it be if I was to put these 2 sprockets on and reused the old chain

Wait for the chain.
You're going to want a rear stand to lift the back of the bike as you'll need to pull the wheel off to replace the rear sprocket.
Not sure of chain length but if it's not the right length you'll need a chain link remover.

my speedo cable looks like it was pinched and cracked at the bottom toward the front tire,

Pull the cable off and pull the inner cable out of the sleeve to see if its damaged before you buy anything.
If the cable has been pinched it might be the drive mechanism on the wheel that's the problem.
If you've got a front stand undo the cable from the speedo, spin the wheel and see if the cable inner turns as the wheel spins.

As for the engine issue it sounds like carby tune, crap in carby of a dirty fuel filter. Hopefully not ignition coils.
Maybe try some metho in the fuel to see if there's water in it from sitting and some carby cleaner but if it sat it could be bad fuel gumming the jets up.

 

[QLDs4]

Can't help with those questions as a don't have a carby bike.
Post pics of the parts and hopefully one of the guys into those models can help you out

 

[QLDs4]

1st pic. should be the sender for your low fuel light.
2nd. The canister under the seat is pollution gear.

It starts at the valve circled, runs to the canister and then to the air box so the engine burns any oily air generated by the crank case.
Some people just put a small filter on the valve.
If the engine has been over filled with oil the canister can have a bit of oil in it.
3.its best to have both of those half bushes in place or the exhaust may, or may not be sealing properly on the gasket.
They go under the cast iron ring that bolts the exhaust on.
Is the other half trapped in the heat wrap?

The diagram is deceiving, the half bushes are there to lock the ring in place around the pipe.

Handy resource for you.

Monster Ducati motorcycle # DUCATI Online Genuine Spare Parts Catalog

www.bike-parts-ducati.com

The parts diagrams are handy and it tells you if the parts are available through ducati.
If the list has a price your dealer can get it for you.

Good to see you getting the boy into bikes early.

 

[QLDs4]

Your problem with the front brake is just the switch which you should be able to get through a dealer. It's on a LOT of models/years of ducs so they might have one on the shelf.
90% of the parts I've ever bought have had to be ordered though.
You should still be able to test the tail light by holding the 2 wires together.

Replace that chain and sprocket, looks old and shitty.
A broken chain can destroy your engine case.
Use pic below for this next bit.
The retainer clip is splined, when you put it on you may need to rotate it a few times to get it on the shaft splines.
Fit it into the groove (red in pic) and you will need to rotate it until the bolt holes line up but the splines on the retainer don't slide out of the groove.
If you move the old sprocket so it's outer edge is against that groove you will see that the centre of your chain should be sitting over the ridge (blue in pic) of the chain guide, not where it is sitting in the pic.
Your new sprocket having a narrower shoulder will move the chain teeth about a quarter of an inch further outwards, which will also move the chain outwards as well.
This will put your chain to the out side of the guide and your chain won't be aligned properly.
Send that sprocket back and get them to send you one with the thicker shoulder.

I'll finish with a disclaimer.
I'm not exactly sure which front sprocket your bike should have but I'm assuming that the old one is correct.
On the supersport 750 it has the thicker shoulder and the 900 has the thinner shoulder.
This is because the 900 has a wider rear wheel than the 750 so the chain needs to be further outwards to allow clearance for the wider tyre.
Hopefully another forum member with your model will confirm or ridicule this assumption.