Thanks for pointing out that in Settings>Devices, it wasn't talking about my personal iOS when it said v.8, it was speaking generically. i had become somewhat disoriented by the whole thing and missed that. 🙂
-- i followed your instructions but it still says the Mac is offline. i signed out of iCloud (though not on the iPhone, only on the Mac). i restarted the Mac (i realize you said to first restart then to sign out and sign back in to iCloud, but i had already signed out of iCloud before i saw your post). I turned wifi off and then back on on both Mac and iPhone. i signed into iCloud.
About the Apple ID, maybe that is somehow involved in the whole problem, or maybe not. My main Apple ID is a gmail email address which became my Apple ID before there was a me.com or an iCloud. This is the Apple ID of record that Apple has, i believe. It's the one i use to sign in to the iTunes/App stores, it's the one i use to sign in to the Apple website, including these forums and if i want to make a genius bar appointment or whatever.
btw, could there be a problem because i continue to use me.com for iCloud instead of iCloud.com, although either one works as an email address related to iCloud? Seems doubtful.
But so, on iCloud, the gmail Apple ID was the default (auto-filled) ID for iCloud and in the past it has worked OK, my contacts and calendars were in there, but today when i logged in, the contacts were almost empty and the Calendar was empty. They used to be in there. i signed out and signed back in with my me.com ID and its accompanying password, and then all my contacts and Calendars showed up. Up to that point, my iPhone was showing up as offline too. After the Apple ID sign in name was changed, the iPhone acted normally in Find My Phone, but not the Mac. I'm wondering if there is some way in which iCloud wants me to log in to my network or my computer or something in a different way, where i am by default logged in with gmail.com.
Or maybe it has to do with information Apple has that iCloud accesses, in particular that the Apple ID i have with Apple is the gmail address.
Just groping around here.
Another thing is the name of my computer/hard drive. The name i gave it when i got it is MBP. It's a macbook pro. I had another MBP a long time ago from about 2007 to 2009 when i replaced it with a MacBook that ran for 5 years and was replaced in late 2014 with the new MBP. The previous MBP had also been named MBP.
For some reason, related to this, i presume, although my current computer is named MBP and that is what it says under the hard drive icon in the upper right corner of the display, someone somewhere, i am guessing at Apple, has named this computer MBP (2). In my Find My Phone on the iPhone and Mac, it says MBP (2) is not online. I had one other incident where i saw this, it was about a year ago and i had some sudden unexplained serious problems with email/contacts (all kinds of spam people being automatically entered into my contacts). At that time, while working with Apple support, i noticed that if i double clicked on the hard drive icon, in the window that opened on the left, in one of the lower categories, i don't remember which one, it listed MBP (2). That is the only other time i've ever seen that. So i have wondered if this could be related to the "offline" thing with Find My Phone. When i was working with Apple support on the email/contacts problem, i told them i saw this MBP (2) thing which troubled me. They had not heard of this before. I was told it probably didn't cause any problems.
Before i did the restarting the Mac and turning wifi off and on, i renamed the computer MBP (2), but that did not fix the problem. I'm going to change it back to MBP.
I was wondering about deleting the MBP (2) from my devices on iCloud Find My Phone and then adding it back on, but after googling, i couldn't find any information about how to add a device.