I am using chlorine tablets through a chlorine feeder to keep my pool under control.

On two occasions I omitted to replace new tablets quickly enough, as the old ones had dissolved and finished.

My pool water had started to go cloudy, and thankfully increasing the dosage, within three days the water returned to sparkling again.

In using an AquaChek test strip, it is reading that although I have a good free chlorine result, my ph, total alkalinity, and stabilizer readings are zero.

What are the disadvantages in ignoring these three last indicators, and what are the advantages in rectifying them please?

There are more experienced pool guys on this forum who will offer additional advice I am sure. My 2 cents worth says that you cannot truely have a PH of 0; that indicates a very strong acid; think battery acid. Possibly your strips are past their use by date? I gave up on the strips and used the liquid test kit where you put a couple drops into two water samples to check ph and chlorine levels.

Agreed - it is impossible to have zero ph and highly unlikely you have zero TA and zero Cyanauric. The strips are duff. Get new, get a different method or take a sample to a pool shop that will test your water.

As a postscript, if you live in an area reasonably well-populated by falang it might be worth posting your town on here. Maybe some kind soul would come and help a pool newbie out. I would certainly do it* within say a 100k of me for a couple of beers and a half day out!

(*not exactly mega-experienced but certainly confident with and equipped for the basic 4 or 5 tests)

Best thing you can do is get a professional test kit. It's fairly easy to get all your chemicals within tolerances it just takes a little time. There is a very good website called troublefreepool.com that can help you. I would also urge you (and everyone with a pool) to add Borax to your pool, there are enormous advantages, not just in water quality but in sensitivity to low chlorine, you can generally get away with very low chlorine for 4 or 5 times as long as you would without it, you can also adjust your pump timer to turn over your water once a day instead of twice a day, the only disadvantage is if you have pets and they use your pool as their main source of drinking water. There are very many swimming pool companies here who have never heard of TA, CYA, Borax etc and just correct Ph and Cl. Actually you can run your pool like this but you might get problems with things like your tile grout dissolving, needing to use lots more Chlorine etc.

Get in a pool with ph 0 and you won't be getting out in one piece.