>>1808020buy a chain wear tool. If the chain is stretched to .75 replace it, if it's 1.0 replace the cassette too.
When you replace the chain, take the rear derailer cage apart and clean the jockey wheel bushings.
drop the chain off the inner ring so it's not engaged with the crank teeth. Spin the crank. Try wiggling it side to side. If that bottom bracket bearing is rough, replace it with a new cartridge unit.
Grip your rims and try to wiggle them side to side. See how freely they spin. If it's rough or loose you should service your hub bearings.
Do the same with the headset. Grip the stem in one hand and the fork in another and test for play/ roughness in that head bearing.
I would straight away upgrade the pedals. I like the MZYRH or Fooker, raceface chester knockoffs. I'd also upgrade the grips. Those ones you have now are worn out cheap shit and probably feel gross. Go for Ourys or ESI.
I like to just clean bikes with a big bucket of hot water+ dish soap and then kerosene for grime that doesn't get. A toothbrush and rags. Isopropyl alcohol is useful for getting grips on and cleaning brake tracks. You also need to buy a grease for lubing bolts and fasteners and repacking bearings. Get one without teflon.
