I would try to get to know scientific/latin names as much as possible, at least at the higher level (knowing a favia from a euphyllia).
This (Aquarium Corals : Selection, Husbandry, and Natural History by Eric H. Borneman) has to be one of the best books I've ever picked up for learning about corals specifically (though I've read and own dozens of them). He used to spend a lot of time on ReefCentral helping people out as well, and is an active publisher and researcher in the hobby.
You might want to try using some GEL thickness superglue to glue smaller frags down, or frags to epoxy and/or epoxy to the rock. the superglue helps in the short term while the epoxy hardens. I use just superglue on most of my frags. Make a ball of the gel at the skeleton, and then stick it to a rock, rock it back and forth to break the film on it so it sticks, and should be set.
You can mount them to the rock, but just be careful because favia will grow on to the rock you put it on, and continue spreading. They will often open up with feeding tentacles, and can sting anything nearby, so plan on the rock being it's own rock after some time.
If you look on my nano build thread, I have a picture of my old 120g tank there. I had a small rock of favia that I kept next to one of the bottom base rocks in my rockwork. It grew and eventually grew to the rock, then took over that entire rock (about 12"x6"x6"), and had sweeper tentacles at night that would reach 6" from the farthest head.
I have a "war coral" favia right now that has some damage to it that I'm hoping it grows in to sooner than later. I haven't been directly feeding it though. You can feed faviids meaty foods BTW to get them to grow/heal faster.