Online emails and folders from anywhere

Hi

I have many emails addresses with my domain name (webmail) + 2 gmail addresses.

I am looking for a "programme" from which I can receive and send all the emails from my multiple accounts from any browser and any computer.

I would like to be able to also import and keep all my email folders stored on my mac mail so they are accessible online from anywhere in the world.

Can icloud do that?

Thanks