With Linux and KVM/QEMU, you can map an entire physical disk, disk partition, or file to a block device in the VM. For my own VM hosts, I use LVM and map a logical volume to the VM. I assumed cloud providers did something conceptually similar, only much more sophisticated.
Files with reflinks are a common choice, the main benefit being: only storing deltas. The base OS costs basically nothing
LVM/block like you suggest is a good idea. You'd be surprised how much access time is trimmed by skipping another filesystem like you'd have with a raw image file
Heh, you'd probably be surprised, there's some really cool cutting edge stuff being done in those data centers but a lot of what is done is just plan old standard server management without much in the way of tricks. Its just someone else does it instead of you and the billing department is counting milliseconds.
Not generally, especially not the super generic stuff. Where they really excel is having the guy that wrote the kernel driver or hypervisor on staff. But a lot of it is just an automated version of what you'd do on a smaller scale