Actually an EV battery voltage will vary base on the State of Charge. Therefore the voltage at the interface between the device providing voltage and the battery will increase as the battery becomes full. The important issue is not to exceed the battery pack maximum voltage which varies by EV. That is typically done by the communicaiton interface which is presumably coming from the EVs battery management system, and is implicit in any DC fast charging system. Every vehicle has a different voltage depending on the pack configuration.
Not much. The physics of charging a battery do not change just because you have a higher/lower voltage pack. If you want to charge a 52V lithum you need to push something more than 52v at it. Usually ~54v nominal, maybe up to 58v for a boost charge. If you want to charge a 400V ev battery you need to push something more than 400v at it. This charge voltage is going to be in a pretty narrow window, and never lower than the nominal voltage of the pack, I'd doubt it would get over 430v, I could look it up.
The BMS on the car is going to request a restriction of current not voltage as the charge state approaches 100%. The available current flow is going to be based on the internal resistance of the battery which increases as it gets charged. The voltage reading at the connector will go down as the current flow is restricted into the batteries, since the resistance goes up. A meter reads the voltage drop across a load, so the closer you get to 100% the lower the voltage reading should be, as the current is restricted, the voltage should approach whatever the nominal is for the battery.
Almost all current vehicles are either 400v or 800v systems. Some of the older stuff, mostly CHAEDMO I think varied, like 240, and 320 and stuff. I know the J1772 AC spec reasonably well, but with DC the rate logic moves into the charging pedestal from the car. You will obviously be coughing up the required charge voltage along with the desired current/rate on the control pin. One of the problems with NACS is the Tesla stations only support up to 500v charging, and some of the newer cars want 800v for maximum charge rate. They obviously charge by bank if they have to negotiate a lower voltage.
Which takes us back to:
If your EV needs 450vdc to charge DC direct, you need to feed it a stable 450V. Doesn't matter what the number is, if you are rolling juice from a solar panel you will have to get the voltage up above (but not too far above) the nominal voltage of the battery you are trying to charge. It will need to be relatively stable or it's likely to get shut down. It ought to be easily doable as long as the car doesn't get pissy if you repeatedly drop output. We are really just talking an MPPT for a 400v battery, the problem is most MPPT's require PV voltages above the charging voltage. So now you need to upconvert or come up with a string that outputs well over 400v. Then it needs to hit the batteries direct and not have any of the electronics in between get mad. God help you if it backfeeds, you will need a good diode.