If you have time on your side, you can also propogate zoas by setting a small frag of them on top of one or more frag plugs and let the zoas grow and spread onto the frag plugs. Once a few polyps spread onto each frag plug, then you can remove the original frag and allow the plugs to fill in on their own. I've been doing this lately. It's kind of a slow process since it involves letting the zoas grow new polyps, but it requires only the smallest amount of cutting (to separate the original frag from the frag plugs and possibly the frag plugs from each other), no glue, and mimimal handling of the zoas themselves.
As for propogating mushrooms, many types can grow a new one from just a small piece of their flesh. Simply cutting the mushroom off of the rock as close to the rock as you can will accomplish this, as it is very likely that you will not cut off every bit of the mushroom's flesh. Then, you can reattach the large mushroom elsewhere. Within a week or so, you should see new mushrooms forming from the small bits of flesh that were left behind. I wouldn't say this works 100% of the time, but when it does, it is very easy to go from 1 mushroom to 3 or more very quickly.
I've seen others recommend cutting the mushroom in half right through the mouth, but I've not tried that myself. Some of those that have tried it have said they've had the mushroom just grow back together.
In any case, if you're not particularly familiar with cutting a certain coral in order to propogate it, I'd suggest trying your hand on an inexpensive variety first. The last thing anyone wants is to attempt to frag their $25 / polyp zoas or $40 / polyp ricordea only to end up killing them.