EV's are not the answer to climate change. They may go a long way towards solving localised air quality issues, which is a good thing but in terms of climate change they are not the answer.
Addressing the vehicles themselves:
Production methods and costs - pretty much on par with conventional vehicles in terms of raw materials and energy input. The biggest downsides to to EV's is the environmental impacts of the batteries themselves in terms of the pollution caused by mining the finite supply of rare earth metals and the end of life recycling processes.
Charging infrastructure - Nowhere near the capacity required. Not just charging stations, but power generation and the associated transmission infrastructure. Unless the energy used to charge them is directly derived from environmentally friendlier sources they are still indirectly responsible for CO2 emissions.
When you consider that a small number of super tankers produce the equivalent CO2 emissions and pollution as ALL THE CARS on the planet why are we wasting our time fighting CO2 production with EV's when time/money would be better spent improving the efficiency of conventionally fuelled vehicles and hydrogen fuel cell technology?
I don't think anyone is saying they are
the answer to climate change. But we have to move away from this pointless logic that we can somehow make fossil fuels incredibly efficient and neutral to our environment. We need to collectively accept that the logical way forward is to wean ourselves off them for good.
The simplest way to resolve the energy capacity issues you describe is nuclear power. The existing technology is incredibly efficient and very clean. This would give us enough time to improve renewable forms of energy and reduce our energy requirements.
The complaints about battery production are valid. But I'd argue the lifespan of a battery (which will improve) swings the argument back in the favour of electric vehicles. Before the pandemic, the UK used around 47 billion litres of fuel for our vehicles. If every car in the UK was electric and the batteries lasted for 6 years (which is incredibly conservative) we'd save around 300 billion litres of fuel being extracted.