Here is a primer on train maintenance. This goes into probably more depth than you will need, but it is good information. https://www.justtrains.com/Service/maint-main.asp
Exploded diagram for your engine is here: https://www.lionelsupport.com/service-documents/ Download "Supplement 1-9" from the drop down list, and see section 3 page 6 in that document. There is a diagram of your motor at section 3 page 52.
There are endless opinions on what to use for lubrication. For what it's worth, I use Mobil full 0W-30 full synthetic, and Red 'n' Tacky no. 2 grease. Note that R and T is not intended to be packed into an enclosed grease box; it should be put directly onto the gears.
To get to the gears, you simply pry out the grease cover (rectangular patch over the rear drive wheel). Remove the two screws in the motor mount (just behind the grease cover) and the motor will lift off and you can get to everything. I like round toothpicks to work the grease out of the gear teeth. Be aware that sometimes this old grease will get hard down in between the gear teeth, like mud stuck in the lugs of your boots, but not appear hard on top. When putting the motor back in, be sure you have the gears meshed. You should be able to turn the motor with your finger easily when the gears are meshed. It is possible to put it together where the worm is riding on top of the gear teeth. No bueno (ask me how I know!)
As for the tender: So the good news is that your whistle at least works! A short circuit somewhere is one possible reason why the whistle might sound all the time. To eliminate that possibility, you should first replace that decomposed foam rubber underneath the circuit board. Hardware-store foam tape is fine. The idea here is to make sure none of the solder points under the board touch the metal frame. Inspect each individual component and make sure that the wire leads for each do not touch each other on the top side of the board. Seriously: I had a board that did not work, and all it was was two of those component leads touching each other. Also, test the tender on the track by itself, to be sure the problem is not in the engine.