Here's my take.
The cardinal, gramma and the yellow (watchman) prawn goby will be just fine together. Six line wrasses will go rogue. It's just a matter of when IME. Your inverts will be the first casualties, many of the fish will follow. A much better choice in the wrasse family would be any of the flasher or fairy wrasses or my favorite (by far) leopard wrasses. I have a pair of Blue Star Leopard wrasses and they are not only model citizens, they are absolutely gorgeous. As an added bonus, they will happily rid your tank of many little pests (flatworms) that can otherwise be a problem.
Firefish will be fine.
The clown will depend on what species and should probably be introduced late in the game due to their propensity for claiming territory and defending it.
A mandarin will depend on your ability to supply it with ample pods (thousands/day) Without a well established refugium it is nearly impossible to do so. Although many can be trained to eat prepared foods, because they don't have actual stomachs, they must graze all day, every day regardless.
The shrimp will all be fine, although you can expect the pepermints to be difficult to see in the tank.
With the correct lighting there is no reason you can't be successful with a RBT anemone. Just make sure your powerheads are protected. Having your prize anemone become chopped up mush is not only quite the bummer, it will pollute your tank badly.
If you develop a bubble algae problem an emerald crab or two can help, but IMO/IME manual removal and nutrient control does a much better job.
As for the hermits - never in my tank. They become destructive quickly. If you really want hermits, Scarlet reef hermits stay small and won't bother a thing.
The pods will come on their own with time and are a normal part of any healthy system.
You might also think about a Tang in the Bristletooth family. They stay small enough to be happy in a 120. I have a Tomini that fits in very well with everybody else and spends it's days cruising the reef picking at algae.
Another to look at would be a Dwarf Angel. There are a number of very nice looking members of that family as well.
What are your plans for lighting/filtration, etc? those choices will also help narrow the possibilities for you.
hth