And Erlang/BEAM that I've used as an example has its own tracing and debugging facilities. (I don't think it has proper multi-tenancy though so it's not like someone can just use it for cloud as it is, but I've just picked it as a closest example to what I think serverless should look like.)
Or you're talking about this from node/server admin perspective? Then, yeah, sure, but unless you're a cloud engineer it's not your business - that's Amazon/Google/Microsoft's problems.
Yes, you do. BEAM will not handle your CPU interrupts or manage your physical memory pages or your USB devices. (The 99 percent of an OS's job.)
I'm sort of oversimplifying it (and probably forgetting a piece or two), but all that's needed is MMU, some minimal network subsystem with device drivers for network cards, and some very tiny VFS - just enough to handle the initrd-like thingy (the rest would be networked storage handled at the application level). E.g. if all we're going to ever run is a single VM that has its own ideas of processes and signals, we may not really need any full-fledged process scheduling or IPC, just the bits to support kernel's own threads.