Are the emissions to power electric cars really better for the environment than the emissions from petrol cars?
It depends on what vehicles you compare and what the exact breakdown of your local grid is, but in general, yes EVs tend to emit significantly less CO2 than your average car even when the grid is not particularly low carbon just because gasoline engines are pretty inefficient.  This plot shows how many MPG a gasoline car has to get to match an higher efficiency EV:



https://blog.ucsusa.org/rachael-nealer/gasoline-vs-electric-global-warming-emissions-953

As you can see the numbers vary pretty widely since different parts of the USA use more or less coal/gas for power, but on average it is very hard to get a gasoline vehicle that is efficient enough to match an EV.