Imagine these batteries in Teslas, that will mean a full charge in about ~10 minutes, which could potentially make all gasoline cars lame.
Look at it this way: Human endeavor consists of intelligent application of energy to mass. One of the three elements are close to being made trivial! It's very easy to get excited about batteries and renewable energy!
As I have an EV, that's closer to my current scenario of charging (once they put in a charger in the office parking lot) 4 hours and going 90 miles. The tradeoff of reduced distance for superior charge time is...irritating.
I have no idea about how credible its claims are.
Tesla is attempting to solve this by building a massive battery storage capacity into the chargers and then trickle charging these batteries when the charging bays are not in use, so this is by no means a problem that has been solved once and for all.
So you are correct your average distribution feeder probably does not have capacity for a 10 mw service. I guess that's not much of a shock.
Charge profile is not linear in existing batteries. A supercharger is 40mn to 80% and 75mn to 100%.
Many people have a mental model of battery charging like a tank of gas or another fluid, in which the first 10% and the last 10% take the same amount of time and effort.
It seems like a better mental model of battery charging would be a pressurized container of a compressible gas: the more you put in, the more it takes to put the next bit in.
However, back in the days of NiCad batteries, some formulations could cope with really fast charges - and in fact would behave better and last longer after a very fast charge than they would after a slow charge.
We're talking about shoving 20 amps into a C cell for five minutes here. You needed to carefully monitor the cell temperature - the charging process wouldn't generate much heat until the cell was nearly full, at which point nearly all the energy going in would convert to heat. 20 amps would heat a full C cell up very quickly indeed.
As far as I've been able to gather (and I have no real special knowledge here and could be way off), the main problem with quick charging is that it heats the batteries a lot, since charging is not a 100% efficient process and any waste energy turns into heat. Heat is bad for batteries, so it could affect their life. However, Teslas have active temperature management for their batteries (both heating and cooling, as required) which should mitigate that.