Fire shrimp do not eat other shrimp, and dont outwardly pick at corals. I am sure that there are certain circumstances that would cause them to pick at a coral, but this is also a possibility with EVERYTHING that you put in your tank.
Gale, the macros that you have suggested do not reproduce sexually and you are correct that most calcareous alages do not, the one exception to this is halimeda.
As far as the algae going sexual it is not something that is easy to to prevent. The algae produces sexual gametes when given a dark phase, and when the algae is ready to reproduce, its cell walls burst, releasing the gametes into the water column. The problem isnt necessairily with the gametes, but instead with the chemical processes that it takes to cause the cell wall to burst. This act requires a great amount of oxygen, so when the algae goes through a spawning event you can see a very drastic drop in pH that is so great it will often kill a lot of your critters. If the pH swing doesnt get them, then the release of a toxin called caulerpacin certainly can. All caulerpa produces this toxin, and releases it if damaged which is why so many of the books on the subject recommend pinching the algae before you remove it so that the algae produces a "plug" that is almost like a clot.
The other danger that keeping caulerpa in a DT is that it can encroach on your corals. The rhizoids (root like structures originating from the stolon) attach themselves to anything and everything in the tank, and can attach themselves to coral skeletons irritating the coral tissue and eventually choking it off.
If you are interested in keeping algae in your display, look into the types suggested by zooid, or consider chaetomorpha, sargassum (if you can find it).
Cheers~!
Jon