The forms will work even if you export your site, but like you said, you need to keep your account live in order to get full support. If you send your forms to mailchimp the forms will work as well.
Check this disclaimer though:
The second point is kind of tricky because it will depend on how and where you host and register your domain. In this case I will tell how I do it and hopefully it helps you in someway.
I have my domains registered on Godaddy and host my websites somewhere else, on my server I point the main domain to webflow so I can host that website with them and if I need to have another website on a subdomain of that main domain I just modify de DNS configuration for that specific subdomain and host that other website on my server or in Webflow if needed.
Besides you’ll have to do it like this if want to have corporate email for that main domain due to Webflow doesn’t support email hosting.
Let me know if this helps.