Grid capacity will keep up with steady growth in demand over the next decades. It's not a problem now it won't likely become a problem. There won't be an overnight spike in growth, just an steadily increasing pace in the roll out of charging infrastructure. Which is typically powered by renewables indeed. Because that's just the cheapest and fastest way to do it. Some grid companies will fail due to years of mismanagement and lack of investment. Some states like Texas might have to swallow their pride and actually connect their grid to the rest of the country (which BTW. would also enable them to export renewable power, of which they have plenty).

Generally, the grid will need to grow a little bit in capacity long term but actually not that much. We're talking 1.x not 2 x or more. And more like 1.2 x than 1.8x. The biggest issues are with the last mile rather than the amount of power. All solvable; just means a lot of work that people will pay for to get done. E.g. solar panels and EVs are a popular combo you see a lot in many suburbs. It makes economic sense to do it. Those EVs are not a burden on the grid and those households are probably net electricity suppliers even.

Having a few tens of GWH of driving batteries on the road could actually help soak up a lot of excess renewable power off peak. In many places this is already something that grid suppliers incentivize and a great easy way to balance the grid. In some cases there are even negative tariffs (i.e. you earn money by charging your car). A virtual power plant based on millions of EVs would dwarf any nuclear plant in terms of instantly available GW and would actually be able to provide power to the grid in case of spikes. One of Tesla's little side businesses that might actually work out. E.g. 1 KW times a million cars would be a about a GW of power. Realistically, you'd probably provide power at the same rate you charge. So something like 5 to 10 KW at home. Millions of cars plugged in when they are not driving (i.e. most of the time) would actually be a pretty awesome virtual power plant. The only snag might be that demand for that power might not be there most of the time because as argued capacity won't need to grow that much. Mostly it's just about stabilizing the grid.

Regarding your second point, recent hurricanes and other natural disasters have quite convincingly shown that gasoline infrastructure is actually not that robust and typically starts failing when these events happen. The added demand for things like generators typically does not help. Basically fuel stations need electricity and when the power goes, they also stop working even when they haven't run out yet. And that's aside from supply issues which typically also become a thing.

EVs are pretty easy to charge. You don't even need the grid for that. E.g. Solar panels on people's houses work fine when the grid fails for example. Many charging stations have solar panels or wind nearby (and batteries). Other EVs can be used for charging as well if the need arises. In emergencies you can even put up mobile charging points powered using batteries or fuel cells. And you can run your house off them as well during a power outage. As EVs become more popular, petrol infrastructure will go in decline and become less reliable. Some petrol stations will close, the remaining ones will sell less fuel. Etc. Especially, remote areas will likely to have more supply issues as that happens.