Is this fresh peat or is it dried loose peat that you are rehydrating? If the latter, I have some notes somewhere that I’ll try to dig out for you in due course. If the former, then so far as the acidifying effect is concerned, it starts its work straight away.
The turbidity you observe is from very small particulate matter : I’ve played with it and it passed through a 53-micron screen! A few thicknesses of kitchen paper gets rid of it (though it’s very slow and hardly convenient for in-tank use!). There’s less turbidity from fresh peat than there typically is from rehydrated. I don’t know about compressed dried peat (pellets, or whatever) because I’ve never played with it.
Other than its effect on pH, peat leaches humic acids into the water column. If it’s anything like leaf-litter (oak, catappa etc.) tannin is leached first ; then as immersion continues, fulvic acids. But I don’t know whether peat does that – it must be loaded with fulvic acids, so I guess the fish must get some benefit from it right away?
Incidentally, I’m playing with some fresh peat at the moment. I was startled to note the presence of nitrite. (It was at a low concentration but, as we know, nitrite toxicity to fish increases alarmingly with decreasing pH). Have you been able to observe something similar with the peat you’re using?
You can use dipslides to roughly ascertain the numbers of aerobic bacteria in your water. The type you’d need is BT2 – they’re easily available and are less than £10 for a box of 10 in the UK.