It is a 10 second cooldowm, but that is still shorter than the time it takes to run to the teleporter and back (more than 30 seconds when I tried it).
You do not need to wait for the runner to leave the throne room. I usually sent all 3 out if I was sending 1, and left after talking to the last one. Even if you just send one runner out, you do not need to wait for him to leave.
As long as I was double checking the cooldown time, I sent Harry out for fanny blossom about 20 times, and he was 65% successful. He came back fine the first 5 or 6 times, then got hurt 3 times in a row, was ok the next 4 times, hurt another 3 times, ok, hurt, and ok the last 3 tries. Either I was unlucky this time, or lucky the last time. In any case, I'm pretty sure I've never had a (fully upgraded) runner come back hurt 3 times in a row before.
I didn't switch to a different herb to check if the success rate went up.
