Good question. Always ice after a workout/game for 30 minutes, even when not sore. If an area is really sore continue Icing off and on for the first 24 hours. After that the ice does very little for the inflamation by itself. Keep the arm warm until you are done for the day.
Ice/Heat cycling works great for flushing out an injured area, by increasing blood flow (Heat) to the muscle, then clearing the fluids (icing) from the area.
Throwing hard and increasing speed - As someone once said on the old eteamz board, every pitcher who throws hard has one thing in common; they really want to throw hard. So you already answered that question yourself in your last post:
So the last week she has been really trying to throw hard and it shows. You can see the effort and speed increase.
Sometimes that is easy to do if you are on a strong team with other hardthrowing girls: Throw harder or sit! Sometimes they only step-up after seeing strong teams in a national tournament and realize how far they have to go to be competitive.
I believe most of the hardthrowing girls started off in really strong rec leagues like West Grove, Hart, Simi, PYL, Northridge or PQ. Most of the pitchers have private coaches since 8U, and they play pretty much year-round with minimal downtime. If you want to play All Stars you have to be one of the best, and to pitch in All Stars you have to BE the BEST!
As far as the rest of it, every other answer you have gotten so far is correct. Which is to say there are alot of different approaches to becoming a successful pitcher, but different approaches work for different kids.
Hard work is a little bit like "The Price is Right", you have to guess as high as possible,
without going over! If you overwork your DD, the results can be disasterous. I believe you can work your DD almost as hard as you want, but build up to it slowly and watch for the warning signs of overtraining.
I know specifically of two eighth graders who have training regiments that are on opposite extremes of the spectrum. Both throw 60 or greater (yes that is correct). Both of them are well known to anyone who watches elite 93s and 94s. They are probably the two of the best 8th grade prospects in the country. One probably throws in excess of an hour REALLY hard almost EVERY day and another 1-2 hours on her other softball skills. The other limits her workouts and probably only thows full velocity 2 days a week, trying not to wear out early.
All that said, my DD is a 10th grader, throws hard and ALWAYS hit her spots. She works somewhere between those extremes. She understands what it takes, and most of the time wants to do it. Unfortunately tradeoffs are sometimes required and life has a nasty habit of getting in the way. But she is a perfectionist (who will tell me she sucks even after throwing a shutout against a really good team) and she REALLY hates getting lit up. THAT is what keeps her working.
What I am trying to say is that great mechanics and regular high quality workouts are essential. The rest is gravy.