Yes, that's exactly what "colo" in the title of this article is talking about. It is short for "colocation center". You just take your server to their data center, plug it in, and let them handle all the physical operations of running a data center.
yes, through depends what you mean with "everything else".
There are "rent a rack" options (you provide hardware, they provide a rack in a datacenter + network switch(es) + management tooling through the network etc. and when asked will replaces RAM/Disks etc as asked). You still have to maintain the OS through depending on the service you get and what you want to do this can be easier then expected (e.g. because networking is handled through their switches/tooling this can makes things easier and if you e.g. just want to run a single application per server there are net-boot options which allow you to do so in a manner similar to running docker containers. But if you want to run your own OCI container orchistrations then it comes with the cost of you having to well do that.).
But if you ask for you provide server hardware and container and they manage all the rest then I'm not sure it exists. It seems like a bad deal for them.
Yes, you can. I used to provide those kind of services on retainer. Actually managing the "low level" parts of "everything else" was always a near rounding error of the cost, though. Managing modern hardware is not time intensive. And then you put a VM/container setup on top and tie it into an orchestrator and it still looks like a a PaaS to the devs.