Generally, you should try to avoid ending sentences with prepositions if at all possible.
So, for example, the first sentence should be, "Off whom do you think the ball is?" It sounds weird, I know. "Off of" shouldn't be used, anyway, since "off" will always suffice.
For the second sentence, try, "The alarm did work for the time at which we set it." Or, you could use, "The alar
No, no, Anon—you are mixing registers badly. The second is possible, but the first is not: that is why it sounds 'weird'. 'Off of' also has a long history of legitimacy.
The alarm didn't work for the time we set it at.-- OK The alarm didn't work for the time we set it for.-- OK The alarm didn't work for the time for which we set it.-- OK, quite formal. I set the alarm last night at 11 pm for this morning.-- OK