When moving up a level in your levels dashboard the level eligibility is based on data from the previous closed month.
When the system sees that the site has made the requirement the levels team will be notified it can take 5-10 business days as they review applications and allocate the needed Level resources and tools to those who have met the requirements of the next level. Once they have you will see the dashboard update.
With regards to Ezoic hosting this is free and has a lot of awesome features - I've linked an article below which has a breakdown of what's included.
Typically we don't provide managed hosting, which means that publishers would complete the setup on their end; the setup can require a little bit of technical work for migrating the files database, so it's worth thinking about whether this would be right for you.
Your best place to start would be our setup tutorial here: WordPress Hosting App
If you've got a lot of content, you're probably going to want to go for option 2 to get started - the Create Blank Site / Manual Transfer option.
These plugins are all good options for migration:
However if they don't work for your specific site, then you'll need to be able to back up your files and database by an alternative method and then connect to Ezoic via SFTP (credentials for SFTP access can be found under 'manage credentials' in the hosting app in the settings area of your dashboard) in order to upload the compressed files to the Ezoic web directory. The tutorial I've linked above has a step by step breakdown on how to do that.