Congrats on the new tank and WElcome to TRT!!!
First on the algea. I would have removed it first. It's most likely dying because there are no nutruients feeding it in yoru new tank. Now that it is dying it will generate nutruients for new algea to grow (a bad thing)
Second, Bristle worms. It's personal opinion some like them some don't. I do they will make quick work of anything that might die in your tank.
Third, Anemone. Your not going to like this but you will need to wait 6-9 month before getting one and on top of that you need INTENSE lighting T5ho or Halide. Just a guess but I'm guessing your tank hs PC or Nornal output flourscent. In that cake there will be no anemone in yoru future and if you do put one in it will not last for long
Last question, I think I answered it above. No anemone at least for a while So add the cleaners first.
On the bright sode there are many low light (assuming you have low light) corals out there the clowns will be more than happy to host. Hairy mushrooms, hammer,frogspawn, torch, toadstool leathers....
Good luck to you with your new tank!