The easiest way I have found to do the shrooms
is to put them on the substrate and let them attach to a few small pieces of that. Then you can glue them with a gel (I have found the Ross brand to be best) type super glue and they'll stay. If you have sand, you can put in a small dish with some fine gravel in it and let them attach to that. With the mesh, cut a 1/4" wide strip and use it to strap the shroom down. Cut the veil in the direction so that the holes don't close up when you pull on it. I put three dots of glue on the rock. Set the coral/shroom on the glue and wet the rock right away. The glue gets hot as it sets and the water will keep it from damaging the coral. Then strap it down with the strip of veil.
When you say "polyps", I'm guessing you're talking about zoanthids or something similar? You can cut them off, taking as much of the stalk as you can, and glue them to rocks or let them attach to substrate material like the shrooms
. Take them out of the tank to cut them as they may release toxic substances. I use a butter bowl with tank water in it. Hold the rock under the water when you cut as they will squirt when you cut them. Also, always wear latex gloves when dealing with zoanthids. I'm sure you've read some horror stories about palytoxin. If you don't get a good stalk with the zoo, don't try to glue it. You'll end up getting glue up on the head and it won't be able to close up. If that happens, it will die. Whatever is left of the zoo on the original rock will soon grow a new head...usually larger than the one you cut off. HTH