Does Publii give you complete CSS control?

Not sure how 'complete' but there is a section for custom CSS and a developer mode that I have yet to mess with.

Do they allow markdown?

Minimal but working on full integration.

this is the first I've seen of Publii. How do you like it so far?

I think its a great for anyone that just wants to get a blog up and running. I am actually working to move my site to Grav as we speak. Grav has a pretty steep learning curve but its been fun. I would not recommend Grav to anyone without same dev. experience but I would for Publii.

I am moving to Grav so I can keep everything synced in my Git repository in case I have to make edits or upload on the road.

Publii is a desktop application.

Thanks for reading!
It means a ton that you took the time to not only read but also leave a comment <3