You can go into the settings for your WC and limit the amount of current that it advertises. That's about all you can do with most vehicles, which lack the ability to control it on the vehicle side. But your Tesla would max out at the same level.
No. But if you hold down the button on your WC (assuming Gen3), it will start a WiFi access point and you can connect to it and configure the maximum current. If Gen2, you need to open it up and set the switches appropriately. See the instruction manual for your WC. If Gen3, the WiFi password should be somewhere in the original box or on the manual, and there's additionally a QR code somewhere on or in the unit with the WiFi password on it if you scan it.
You really shouldn’t be running a 50-amp circuit with only a 100-amp service panel. It will be better if you install a 14-30 (30 amp “dryer”) outlet and use a 30-amp breaker. Using the Tesla 14–30 adapter you will get a 24-amp charge, which looks like it will be within range. There is no harm in running 6/3 wire, especially if you want to keep your options open, although a 30-amp circuit only needs 10/3 wire.
Why not? The panel can easily handle it, as long as the other loads aren't all on simultaneously. Why limit to 24A (30A breaker w/ 80% rule) when you can charge at 40A? I highly doubt that all of the AC units are going to be running on high at night, and on top of that, the microwave is unlikely to be on for longer than 2-3 minutes. If it's still a big issue, there's always the option of getting a service upgrade, but if all of the major appliances are gas, I don't think it's going to even be an issue. A lot of appliances don't actually draw as much current as indicated on their nameplate either; my central AC unit for example draws ~13A.
This is a reasonable compromise. Besides with a wall connector you will have the option of dialing it down to 30A. And with a wall connector you only need a standard breaker ($10 versus $100+) and no commercial grade outlet at around $80! And I think there is still a federal tax credit if you install a wall connector, form 8911 I believe.
Is your service line overhead or underground? If it's overhead, doing a service upgrade is cheap (and by "cheap" I mean it should be able to be done for under $5K). If it's underground and requires trenching, it will easily run into 5 figure territory.
So my 400A panel was about $4K (that included materials plus labor). Then I had about $7K worth of trenching costs (that's why I went all the way to 400A instead of 200A; I don't ever want to have to do that again). and the 200A subpanel cost around $2K. But 200A panels are much cheaper. And I'm not sure what the labor is in your area. It's high here because of living costs; it's probably lower in your area. Doesn't hurt to at least get an estimate.
Keep in mind that those DCC boxes cost around $1K, plus installation. So you can spend money on load sharing, or you can spend money on service upgrades. A service upgrade will cost more than a load sharing device but any money spent on load sharing devices cannot later be spent on service upgrades if you change your mind. That was kind of the dilemma I faced when I was trying to decide if I should put a subpanel with more breaker slots and see if I could have two EVs on my old main panel or just bite the bullet and do the service upgrade. I chose the latter option, but I have an electric stove and oven. At least it sounds like it wouldn't be as painful for you to do a service upgrade because your service line isn't underground.
But it's just how this works. The charging points don't get controlled, so that's not what you are controlling with your phone. They announce how many amps are available, but it's the car that is what you are controlling to turn down the amps. There are some few kinds of charging devices that let you switch their configuration somewhat easily as to how many amps they will announce, but that's rare.
It's not really dumb, because this is a really weird and obscure circumstance where anyone would have any reason to do this. And it's not really an appropriate thing to do anyway, as the charging device should be matched up in what it is offering to the circuit level it is on. So this shouldn't really be a normal feature of this kind of equipment. And if anyone would be doing this, the more proper place to do it is from the car instead of the charging device. But anyway.......you can, but it's not quick and simple. Tesla's wall connectors have a wi-fi accessible interface. So you can use your phone, connect to the wi-fi hotspot of the wall connector, and change the configuration to turn it down to one of the lower settings.
Maybe not a person dynamically changing the EVSE advertised charge rate but it's something you want it to do when the power source is from your own solar array. You want the EVSE to advertise the available solar output (minus other things being powered), at any given instant, so you don't have to draw and pay for power from the grid.
No, you don't ever want the EVSE to advertise that there's more current available than there actually is, so the solution would be an EVSE that dynamically adjusts its available current. And this exists in some sense when EVSEs do load sharing. But there is no commercially available home EVSE that can look at (total amount of load on the panel - total load currently going through the EVSE) and then adjust based on that. Think about how much this would cost: you need current detectors on the service line and control circuitry that dynamically adjusts to the input. Telling the car to throttle back is something that's specific to Teslas and quite frankly I don't know why they allow their cars to do this. If your EVSE is advertising more current than is actually available, that's an issue that you need to correct because it's unsafe. And furthermore, this "feature" allows people to game the system on public EVSEs that have idle fees when they finish charging; turn it all the way down to 5A and just let it charge all day so you can park in EV charging instead of letting someone else charge.
