Governments need to invest money for all types of infrastructure...

Governments need to invest money for all types of infrastructure in order to kick start the industry. They do it for many industries and services.

Do private companies build new roads, railway lines, ports, airports, power stations etc without government assistance ?

Just because many ev owners won't need a servo, that doesn't mean there shouldn't be infrastructure for them. There certainly won't need to be as many charging points as there are petrol bowsers now. And, they won't have to be concentrated in particular areas either.
Wherever there is a parking spot and a power supply, that can be a charge point. You can park your car and walk away while it refuels. You can't do that with petrol.

Once again demonstrates the flexibility of an ev system.

The average ev owner should be able to top up at home, at work or even in a shopping centre while they shop so unless they are doing a long trip they'll always have a full tank.

Lot of CO2 produced ? How much exactly ?

Yes, produced once for the changeover. Unlike petrol which continues to pollute for ever.