This is almost certainly a function of the hardware, so your three questions will have an IBM answer.
Generally, you couldn't expect that a physically powered off server will automatically power itself on.
The obvious "health" issue is to ask if there is a UPS, and if that UPS has logs. I've seen more than one "my server shuts down" type issue that was the result of bad power. Assuming that's not the issue, does the server have a redundant power supply? If only one, it's probably that which has failed, and IBM should be able to replace it.
On #3, the expectation doesn't make a lot of sense. In the case of a physical power off, the OS doesn't have any time or ability to log anything. Whether the hardware has an integrated log which might note "powered off" is a question for IBM.