Parodinal doesn't use sodium carbonate -- that would be an accelerator alternative to sodium hydroxide (the core ingredient in your drain cleaner), borax, metaborate, or even just sulfite (D-23 uses sodium sulfite as both preservative and accelerator). If you had p-aminophenol in that form, you could probably make a (rather slow) developer with it using sodium carbonate, but it wouldn't have any advantages over Parodinal other than having less hazardous ingredients. But starting from paracetamol/acetaminophen, you need the very high pH to convert the pain medication into the developing agent -- I'm pretty sure sodium carbonate, at 10.6, isn't alkaline enough.
The soda ash for swimming pools is just the thing for making Caffenol. Caustic Soda is the right stuff for Parodinal. BTW, you can probably get sodium thiosulfate as chlorine reducer at the pool store, too -- and there's your simple fixer. The drain cleaning liquid you used probably contains a lot of sodium silicate (to protect pipes from the sodium hydroxide), which might have effects on development (I'm not sure).
It's possible to use Parodinal without the sulfite; after dilution, it has very low sulfite concentration in the working solution even at 1:25. However, it won't last reliably, I'd be suspicious after even three days. You could try reducing the quantities to fit with two Panamax tablets to make concentrate suitable for a single developing tank fill -- you'd wind up with about 17 ml of concentrate, which would be enough to dilute 1:25 into 425 ml of working solution, or 1:50 into 850 ml (the former a little more than a 35mm tank fill, the latter as much as 3x 35mm or more than needed for a 120 roll). You'd mix the stuff, cool it (after mixing the caustic soda), and use it as soon as the solution turns a distinct pink -- might be good as soon as it's down to room temp, since I recall the pink coming on almost instantly while adding the lye. You do need to make this as concentrate, then dilute; if you use working solution volume, the alkali probably won't be strong enough to convert the n-acetyl-p-aminophenol into p-aminophenol in a reasonable time.
I haven't used it without preservative, because I have fairly easy access to sodium sulfite in the USA, but I have no reason to believe it wouldn't work -- but I wouldn't expect it to continue to work for more than a day or so.
BTW, the Calcium Hardness Decreaser seems to be similar to Calgon; it would be useful in mixing chemicals with tap water rather than distilled, but I haven't any idea how much you'd need.