Dumb question but when one says I'll be home after 4, does this mean 4, 4:10, 5 or what time?

It means any time after 4. It could be 4:01 or it could be midnight.

It means they do not know the precise second they will walk through the door but they are confident that in no way will it be before 4pm. if someone says they will be home after 4 they don't want you to start calling them or showing up at 4:15

It means 4:12:37 exactly

It means they won't be home before 4.

after 4 that mean it could be 5 or even 6.

That's totally ambiguous. No telling when after four. Which is why I typically tell someone, "I'll be back before five" or similar. That at least has a definite cutoff time...five o'clock.

Anything prior to 4 pm is not possible.