You have listed all the things we routinely worry about.
Chlorine needs to be removed, usually by converting it to chloride. This is done by using a dechlorinator found in almost all water conditioners.
Chloramine needs to be removed. Water conditioners split chloramine into chlorine and ammonia, and remove the chlorine usually by turning it into chloride. But the chemical that splits chloramine and removes the chlorine part leaves ammonia in the water.
Ammonia in tank water can come from splitting chloramine and from fish waste. When it comes from fish waste, ammonia-eating bacteria and plants remove it as soon as it appears; there may be trace amounts presents at all time but in such small amounts that we cannot detect it.
Ammonia from chloramine is a different matter as that is added all at once rather than in tiny amounts 24/7. For this reason, many water conditioners contain a chemical which detoxifies ammonia for around 24 to 36 hours, and the bacteria/plants should have removed the ammonia before the detoxification wears off.
Nitrite should not be present in a cycled tank. This is only made by ammonia eating bacteria converting ammonia into nitrite; it is not added with tap water unless there is something wrong with the tap water. The only time nitrite should be in a fish tank is when the fish keeper is doing a fish-in cycle, and then the fish keeper should do water changes to remove it, or add salt to protect fish from harm until enough bacteria have grown to remove nitrite as soon as the ammonia-eating bacteria make it.
There are products which claim to detoxify nitrite, again for around 24 to 36 hours by which time the nitrite eating bacteria should have removed it. Seachem Prime and API Aqua Essential both detoxify nitrite; there may be others. These should be used in conjunction with water changes to protect the fish from the nitrite made between water changes.
Nitrate is the end product of the nitrogen cycle. In nature more bacteria convert nitrate into nitrogen gas but these don't often grow in fish tanks. Water changes are done to remove nitrate, though both Seachem Prime and API Aqua Essential temporarily detoxify it.
When a tank is heavily planted, very little nitrate is made in the tank because plants take up ammonia as fertiliser and they don't turn it into nitrite and on to nitrate.
Many places have high levels of nitrate in tap water. The US allows 45 ppm on the scale used in fish keeping, for example. The only way to keep nitrate low in such places is to remove the nitrate from tap water before it is added to the tank.
Metals are present in most tap water, some places have higher levels than others. Most water conditioners contain a chemical which binds metals, so they are no longer free in the tank water.
A number of fish keepers have tap water which they feel would be detrimental to fish. Maybe there's a lot of nitrate or metals; perhaps the water is very hard and the fish keeper wants to keep soft water fish. One solution is to use reverse osmosis water which will remove almost everything dissolved in tap water. Some use 100% RO water, others mix it with some tap water, and others add remineralisation salts to put back small amounts of minerals.