Missed Base/Appeal

[Lapopez]

In general, how much time must pass after a missed base before it becomes an appealable? I understand the mechanic at the plate but a little unsure at other bases. If a runner is trying to return to the plate, it would be obvious that he is doing so because he thinks/knows he missed it. But at other bases he could just be trying to return safely.

1. Slow do-or-die roller to F6, BR beats the throw but misses first base. Base umpire calls safe. F3 knows BR missed the base and immediately turns to BU and says, “But he missed the base.” Is that sufficient for the appeal?
2. Base hit to right. BR rounds first, but misses it. F9 throws behind him. Can F3 immediately (with the ball and touching first base) appeal or has insufficient time passed that he is still obligated to tag the runner?