1) The answer is yes, the switches are fully manageable from the cloud platform. However, Meraki doesn't really work with traditional configs as you know from the Catalyst series. The configuration is done through the dashboard, not via a text file. To avoid repetitive tasks in the dashboard, this can be done more efficiently thanks to templates or starting from a copy of an existing configuration and the use of tags (on ports, devices, networks, etc.). For automation purposes there's also the dashboard API and the new OpenAPI SDK's.
I suggest you take a look at the Meraki youtube channel and look at one of the webinars. That way you'll get a better idea about how it works. They end all webinars with a demo. Perhaps this one:
Meraki's philosophy is quite different from traditional Cisco but it's a very powerful way of addressing networking. Once you've seen the demo you'll see what I mean.
Most of the switches do have a management port. However that's only to do the very limited local configuration necessary to get the switch connected to the Meraki cloud (Static IP, default gateway, DNS settings, Proxy). More info on that here:
https://documentation.meraki.com/zGeneral_Administration/Tools_and_Troubleshooting/Using_the_Cisco_M...
2) Not that I know of. The only thing I do know is that the integration of Meraki into DNA Center will become deeper over time. DNA Center is Cisco's new management platform to do networking in a software defined way. I think over time there will be a cloud based version of DNA Center. There is no on-prem version of Meraki.
