As long as the website is in the account you upgrade, then yes. Keep in mind that the “Super Premium” plan you mentioned does not have unlimited bandwith; that’s the “Ultimate Premium” plan, Super has a 250GB limit.
I’m not sure what you mean here, but you could try and see if InfinityFree’s free plan is enough for your site, and if you hit any limits and want more along the way, then decide to upgrade.