Hi Hugo!
The anemones aren't a danger to fish, but can become an annoyance to corals and their keepers. The rock _can_ carry fish parasites, but adding medicine to your display tank wouldn't be a great way to handle them. The best way to ensure that the tank's safe for fish is to run it "fallow" (without any fish) for 76 days. Velvet and Brooklynella parasites will die without a fish host in six weeks, while Cryptocaryon (ich) parasites may go to 72 days - so the recommendation of 76 days allows for a little wiggle room. Keep in mind that adding anything "wet" - snails, crabs, shrimp, corals, etc... starts that 76 day clock all over again.
While you're doing that, you can also set up a quarantine tank for the new fish, and keep them there (in this tank, you can add medicines when needed) until you can introduce them into the display.
~Bruce