Adding water and sugar to secondary fermentation

The generally approved advice is don't dilute beer post fermentation - and that advice is "not wrong". However it depends on the type and gravity of the beer. I have regularly dissolved the priming sugar in (say) 1 Litre of water and added it to the brew before bottling. I totally recommend dissolving the priming sugar in a minimal amount of boiled water (pasteurises the sugar ) - so some dilution is certainly not fatal. How much dilution can be sensibly done is another question. 5% (ie. adding 1 litre water to 20 litres of beer)is not beyond reason but above that the effects will be noticed if compared to the original beer. If the original beer was brewed with a high F.G. and with much flavouring (hops/roast grains) then it will stand more dilution before it becomes noticeable. Diluting lagers just makes the beer watery and is not an improvement.

However I have seen many 24 litre beer kits made up to a lesser volume (eg 18 litres) and then diluted to 23 litres post ferment. This was done for similar reasons - the FV was rather small and filling it with 23 litres was too much. So it was made up to a lesser volume and diluted to taste afterwards. So one can ferment in a more concentrated mix than specified and adjust FG afterwards. Why they couldn't just get a bigger bucket was open to question....

You can. Don't do it.

Transfer beer to bottling bucket just before bottling. Add priming sugar, let it dissolve. Bottle. Bucket will be partially empty most of the time anyway, because you are bottling. If you want to rack to secondary, just do it, but don't use bottling bucket, use regular one, and don't worry too much for head space. That's all.

If you will add water and sugar in amounts that will not change ABV, you will only have 19/24 ≈ 80% of taste, aroma, colour, head etc. Sometimes it's good - when your beer is too overwhelming. That's why some Belgians use sugar. But that's a rare situation.