There shouldn't be any cadmium in your plumbing. Copper while actually a nutrient in very very small doses, would only be a problem in severely corroded pipes where cold water isn't helping you.

Nobody in the last century+ has lead freshwater pipes.

That said, some of our underground infrastructure is very old, and those old iron pipes had fittings sealed with lead and oakum.

Water flowing through such pipes have pH and chemicals carefully controlled to avoid that lead corroding or dissolving. The Flint, Michigan disaster was a direct result of not managing water chemistry correctly, but there are hundreds if not thousands of communities at similar risk who are kept safe by water scientists and engineers doing their job correctly.

That said, hot water tanks do accumulate minute quantities of undesirable metals over time, and depending on a wide variety of variables between the water source and your tap it could result in unhealthy levels of things you don't want to consume.

So yeah, don't cook or drink from the hot water tap.

If you have a high pressure hot water system, then the heater doesn't touch what comes out of the tap. In those you have a closed system from the heating to a tank. That tank contains fresh water, but the heating loop only interacts with it via a heat exchanger.

Yeah that's not been true for about 50 years.

We replaced all our lead, and it's a legal requirement to if you find a lead pipe in a system, replace it no matter what (even in listed buildings) or disable the outputs entirely (the latter is more common in VERY OLD buildings, with people then adding a new system somewhere else, sometimes with exposed pipework rather than having to potentially damage walls.)

We also just don't do hot water tanks any more usually, instead doing on-demand boilers.

Does mean that the hot runs cold for about a minute, but it balances out

I've never seen a dishwasher with 2 supply lines, they usually only hooked to hot.

The steam that comes out of dishwashers I've used after washing would seem to indicate otherwise. Wouldn't that temperature shock be dangerous to the ceramics?

It mostly depends on where you are in the world and what the wiring is designed for. 220V heating elements are abundantly powerful enough to heat water of any temperature to a useful temperature within the early stages of a wash cycle, and dishwashers with such heating elements are usually designed for cold water, for consistency, because the water in the pipes is always room temperature at first anyway. In places where the dishwasher is built for, and will be connected to 110V electrical supply, they will need the water to be pre-heated (including running the hot tap at the sink where they are plumbed from). If you read the manual, it almost certainly says so.

No matter what voltage they are designed for, they are almost exactly the same in all other respects. You might assume your dishwasher is smart enough to know what temperature the water is and that its magic electronics can run the water long enough or run the heater long enough or do something to make sure it gets to the specified temperature at some point before the cycle is considered done, however in basically all cases it does not, despite all the marketing bullshit trying to tell you how smart they are, they are actually very simple machines and they operate on nothing but very simple, factory-designed timers and cycles in all but the most esoteric designs. They are not smart enough to properly heat the water and almost none of them even have any sensor to detect the temperature or control the heating element in any useful way besides hopefully making sure it doesn't burn your house down. They work because the combination of the heating element and the water supply together are enough to eventually make the water hot enough to wash properly. On 220V it's easier to specify the use of the cold water because that is actually a pretty consistent temperature and the necessary heating times can then be set pretty reliably at the factory. On 110V you have to use hot water, and you have to make sure it's actually hot in the pipes when the machine starts filling. The latter is obviously less desirable, but it's the only way to get a proper wash out of 110V dishwashers. It's a crapshoot, North Americans don't generally know or do this, and the quality of the wash suffers accordingly. But they simply don't make them any other way. Maybe they should change. But they haven't. This is what we're stuck with.

So basically if you have 110V dishwasher you need to hook it up to hot water and make sure the water gets hot before it fills if you expect them to wash properly. That's just the reality of how they're designed. 220V = cold water, 110V = hot water. That's basically universal in the regions where each power standard is used. Unless you take a European/Asian 220V dishwasher and run the 220V wiring to hook it up in North America intentionally, but nobody actually does that, and you're not going to find it was done in your house by surprise.

I can't speak for outside the US, but in the US your dishwasher needs to be hooked up to a hot water line. The detergent won't dissolve properly under 120ºF - 140ºF and they are restricted from using enough energy to get from "cold" to that temperature. Most of the manufacturers will even print in the manual that the water temperature coming in needs to be 120ºF so it can get hot enough to perform all functions.

If you hook up a US residential dishwasher to a cold supply line, you will be hand-washing all of your dishes.

Really not even that expensive. I just installed one and it was like $1400, but it gets a fuel efficiency rebate of $600.

Here they are ubiquitous, and yes I have seen commercials for ones with a tank inbuilt, which is just stupid IMO as you have instant hot water on demand.