[Electronic M]

Welcome aboard!

Diodes are ABSOLUTELY 'directional' (the correct term is polarized). The plumbing equivalent to a diode would be a one way valve, and if you connect them backwards your electrolytic capacitors will explode and other rarer parts could be damaged, as soon as you apply power. Electrolytic capacitors are polarized too and will also explode if they themselves are connected backwards.

As per your ballast compare the pin-out of the balast on the TS-4J schematic to the one in the schematic of your set, and IF they are the same AND the two sets have the same tube heater wiring scheme then it should work. If not just use power resistors of the same value listed for the ballast sections in the schematic and it will work fine.

As per the speaker fabric please define what you mean by 'restore'. If it comes off the board easily you can soak it in water to get the dust out, and stretch it taught over the speaker board to make it look nicer. There also may be reproduction cloth available.... Though from the picture it looks fine to me as is.

As per the bakelite that depends on condition. Light dirt and scuffs can generally be dealt with using windex and novus polish. Heavy scratches and fading/stains/sun bleaching can be dealt with by sanding them off, and then sanding with progressively finer grits of sandpaper until the remaining haze can be polished away....Banderson is the expert on that and had a great post about it a few years back.

EDIT: Bakelite is a rather amazing plastic in that it is impervious to heat, and most chemicals, and aside from being a tad brittle (don't drop that cabinet off a table and expect it to land in one piece) it is essentially indestructible.