Not sure about 2 - What are your arguments for this?
If the status page relies on getting updated information from the service, it may not even notice when the whole thing just crashes and goes down in flames. Attempting to do some predefined calls to the service to evaluate whether it is working correctly appears like a better solution?
Yea I was wondering about that comment too. I mean you can do both. Your status page should be static, updated by a service which both polls and accepts information from your services. You ideally want to go yellow if one of the two fails.
But yes, in general, the status page and status services should be entirely on their own independent infrastructure; and in a different data centre. A number of providers offer independent status page services. If your entire company runs off Digital Ocean, your status page/services should probably be running on Linode or AWS or whatever.
If the status page relies on getting updated information from the service, it may not even notice when the whole thing just crashes and goes down in flames. Attempting to do some predefined calls to the service to evaluate whether it is working correctly appears like a better solution?