The water should definitely not be higher than the mother's body temperature.
With this proviso, the water should be kept at the temperature that makes the mum feel comfortable.
On our first birth, the mid-wife was in the pool with us, and as my wife started to feel too cold asked them to turn the hot tap on, who fobbed her off with "in a little while".
DW "Alexander, tell them to put more hot water in. I'm cold!"
A "Put more hot water in, please."
It helps to have a supportive partner around.
The depth of the water should be deep enough to support the mothers torso if she is sitting down in the water.
Any disinfectant in the water I would say is a bad idea. In most Industrialised countries, the water is clean, and if it has been heated on its way into the tub, then clean enough. The germs that the baby will encounter from the parents, it will encounter anyway, soon after birth. Just make sure you are both clean when you get into the pool. Washing with handfuls of salt prior to getting in is the best way, carefully washing off any salt that remains on the body. Don't even think about putting salt into the pool. It is not enough the neutralize any bugs, unless you put in really loads, and by the time you have put enough in, the pool has become a place to shock the infant, possibly to death, as any open wounds will be very painful. If the dad decides to get in the pool, (I recommend it) he should wear trunks. (Reduces the number of hairs that have to be scooped out.)
Speaking of scooping, make sure you have a hand held pool scoop or tea strainer to take out any poop that leaks out.
You should not worry about the baby breathing in the bath water. Nature has taken care of this for us.
As the baby comes out, it's lungs, wind-pipe, nasal passage and mouth are filled with ambiotic fluid. Moving from the womb to the water is little different for the baby, and it will not try to draw a breath until it gets to the surface, and then only slowly. The ambiotic fluid protects the young lungs at this stage. This is as nature intended, and not to have it sucked out. This fluid is absorbed by the body, and breathing begins gently, not all at once on a raw lung. There maybe "matter" in the mouth, in or around the nostrils, and this can be wiped away with your finger or swallowed as the child takes its first suckle.
Sometimes the child cries, sometimes not at all.
Our first was as slippery as soap, and when she got to the surface, began to draw breath, opened her eyes immediately, gave one cry, (more of surprise than anything else,) and watched me for the next 20 minutes before looking around the room. She was not interested in the nipple, more about the gentle April dawn creeping through the bamboo blinds into our pool.
Our second was sticky. She did cry, and went straight to the nipple. We did not manage to get the music on early enough, and the lights were still on, (she came out so quickly and easily, we were hardly ready), and if I could do it again, I would make the pool bigger. We did have a couple of mid-wives present. They were there more for curiosity than anything else, as they had never seen a water birth before, but heard that it is done on the National Health in the UK. Technically, what we had done was illegal, so we rang them as we got into the pool, so they would not get into any trouble.
The water pressure prevents undue bleeding when the placenta comes out. This should never be pulled or tugged.
In fact, I go further than that by suggesting that the umbilical chord never be cut until the placenta starts to come off of it's own accord. The reason for this is that it gives the new-born infant the opportunity to get oxygen from two sources, one rising, one dwindling. At about the time that the lungs are fully inflated, the placenta comes off. The two do not always co-inside exactly, but nature has done a pretty good job on the timing front.
When the chord is cut, use really sharp scissors. The chord is rubbery, slippery, and VERY resistant to cutting. We used a huge pair of sewing scissors.
As for eating the placenta, the benefits, the preparation and storage of. . . this deserves it's own thread which I am now preparing.
Hope this helps.