Hey JJ,
Nice Home Page, nice to see someone that spends a little time on their homepage (unlike myself... ...who's home page has been under construction for the last 9 months... heh heh heh!)
Not interested in the prize, but here is a most likely ID list, some of them are hard to ID without seeing the skeleton with absolute clarity.
1. a slow pulsing specie of xenia, prolly S. enlongata, there are over 60 species of this Genus that are id'd primarily by the appearance of the spicules in the soft octocoral tissue. This is a related spp. to Item No 6, which goes by the common name of Red Sea Pulsing Xenia, sorry, I don't have much more to go on either of these two. Id'ing these two without a spicule analysis can limit them to about 5 or six species names for each, the morphology of these two is the only ID mechanism you have so far.
2. Prolly Lobophyllia hataii, also known as colored brain coral or carpet brain coral, but could be Mussismilia from eastern SA coast. (Atlantic)
3. Well, Actinodiscus is probably as close to an accurate ID as you will get, although based on appearance, it is prolly Actinodiscus (or Discosoma, names are changing) ferrugatus, usually red brown to rust colored and often with a pimpled surface of contrasting color. The problem with these spp. naming these is that their morphology can change based on current, nutritional status, and lighting conditions. To make matters worse, there are few supporting structures (i.e., skeletons, spicules, etc.) to aid in the taxonomic separation of these corallimorphs. Much of the literature is VERY dated, making their ID beyond the Genus difficult if not altogether impossible.
4. Sorry, but that is most likely NOT Heliofungia, even a very young one. Most likely some form of anemonea, see Delbeek and Sorung, Vol 1, I would need to see the scale of the creature and how it came to the tank (was it a hitch hiker?) It could be a Discosoma spp. mushroom, prolly D. sanctithomae, but hard to tell without some form of scale and a knowledge of it's past and acquisition.
5. Sarcophyton, prolly S. Elegans, they are usually either Yellow or Cream colored and have the pincushion appearance during the height of the photoperiod. Often pulling back and deflating at night, even to the extent that they may look sick. Very common for them to do this in response to the immersion of your hands into the tank without proper scrubbing and copious rinsing (even to the point of using a baking soda or salt as a scrub instead of soap) These are easy to propagate, and hardy in the aquaria, but often difficult to positively ID without microscopy of the sclerites due to many morphological variations from color to general shape.
6. Prolly Red Sea Pulsing Xenia spp. see No 1 above. These may start and stop pulsing depending on several different parameters.
7. Another Discosoma (Actinodiscus) usually differentiated from Rhodactus and Ricordia spp. by the smooth margin, although this is not absolute. Eric (Borneman) says that DNA analysis will prolly sort out these taxonomic issues, but for now, Ricordia usually have a tentacle-like fringe, discosoma(Actinodiscus) are smooth.
8. another Discosoma
9. Heh, this is a TRICK question, this is prolly sinularia, but not what you are used to, This is commonly known as cabbage leather coral, a member of the most predominant genus of soft octocorals, with prolly the most differing morphological forms as well. Specifically, this is Sinularia dura, a very distinctive and hardy sp. for your tank. I am assuming that this is directly attached to the LR and does NOT have a skeleton underneath, if it does, that changes everything.
10.
Sarcophyton Elegans, see above
11. Sorry, not star polyps, but button polyps, a colony of Zooanthus spp. buttons. Hard to ID the specific Species without seeing what the mat underneath looks like. Many are rapid-growing encrusting spp. with a mauve to purple mat, some are connected by a system of channels, some by little root =ilike appendages, many of these morphological features will determine (or at least narrow down the choices) which sp. it is most likely.
12. common Yellow polyps Parazoanthus axinellae, usually occur as single unconnected polyps with 26 tentacles on each polyp. Although there are many spp. of Parazoanthus, most of the others occur in conjunction with other creatures of the coral biome (i.e. sponges, occasionally on dead gorgos)
13. Definitely a sarcophyton, although possibly a Lobophyton, hard to tell in it's current state. One of the Alcyonians without a doubt. One of the differentiating characteristics of Lobophyton and sarcophyton is in the capitulum. in Lobophyton, the capitulum tends to form crowded plated or finger-like folds across the upper surface. Stalks are generally low, short and fat. The polyps are not Well-stalked calyces, but are occasional and sparsely placed (or have reduced stalks) and are completely retractable. Due to the club like spicules of Lobophyton, the tissue of the stalk often appears granular or bumpy, whereas the Sarcophyton often appear as smooth with fibers embedded in the tissue.
14. Now THAT is a
green star polyp, encrusting variant, prolly (based on your description of the mat) Pachyclavularia violacea. The old id of this was Clavularia viridis, but based on several morphological variations, P. violacea is more likely correct (Clavularia have feathery pinnules, have a thin, less rubbery mat due to a relatively small number of stolons between polyps, and P. have a smooth tentacles surrounding an often contrasting colored oral opening. The half sphere shape of the colony is prolly due to the item that it is encrusting over.
This is the best I could do on short notice, I still have to finish the lab write-up for Eric's class. :

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Hope this helps