So, the plan at this point is to replace all the fuel lines and filter. Filter is pretty new and still clear, but I have another one.
Cut or remove your old fuel line. Probably hard as a carp. Take it to an auto parts store for replacement. Get a couple extra feet for fuel filters and shut off valve installs. Install ALL new fuel line and filter, tank to carb inlet.
I did notice this morning that the fuel filter was empty before start up. Is this normal?
No. Sounds like lack of fuel delivery. Reason I told you to pull the fuel line off AT the carb inlet and test. Possible dead pump if your engine has one or clogged hose, tank or filter.
If I do spot trash in the tank, what's next? How to clean, is it a chore to remove? It looks like it?
If you see trash it HAS to come out, end of message. Could take time. It's a 2 second job on a Snapper. Could be a 2 day job on a Kubota I don't know. Hopefully it's simple you can follow the lines and bolts. Maybe one of the others here has worked on a machine like yours??
What is the electronic looking device attached to the bottom of the carb? What's it do? (see, not a mechanic lol)
That is an anti backfire solenoid. Prevents excess fuel in the cylinder and or muffler from making a loud near gun fire sound which my neighbors LOVE. Stops fuel flow to the carb main jet when you turn the key off. Key on, sends battery voltage to this solenoid, retracts the solenoid plunger, passing fuel to the carb main jet. Key off, kills battery voltage to solenoid, plunger extends, stopping fuel flow to the main jet.
Should I replace the fuel pump even though it is working? It works when the engine is cool for sure.
You need to percolate on that one. Read what you typed again. AND the same reason I asked to pull the hose off AT the carb inlet for testing. THIS will verify if your pump is good or not. You need to crank the engine most likely for your pump to work. Could be an electric pump, not sure. If it is a pulse pump, need to crank the engine over.