Never underestimate the White Devil. Never. Nanoha can take the punishment, and she will always overpower Fate. Nanoha is a bombardment type. Bombardment types are not glass canons like in every other series; they're the howitzers. They're both Aerial Mages, they both have a huge magical output (Nanoha moreso), but Nanoha is stronger at long range blasts.
Fate isn't the type of mage who can compete with Nanoha's type. She can destroy Nanoha in close combat, but when she tries to go for the longer range, long casting time finishers, she just can't compete.
Like Raising Heart said, they beat Fate with superior tactics. Nanoha, Raising Heart and Yuuno knew Nanoha's strengths, and developed them fiercely. Fate didn't fight the way she beat Nanoha earlier. She should have closed in and pressed her hard. She fought poorly, and Nanoha capitalized on it. Everyone in the franchise underestimates how much output Nanoha can produce and her range.
Earth-born mages are just better. Probably because they are so rare.
Looked like an unspecified kind of radiation (Neutron, hawking, who knows) to me. They were working on a reactor. There wasn't a scratch on the cat, nor was there any on Alicia. More importantly, there was no damage to the buildings. The rescue team was wearing hazmat suits. It looked like a magical explosion, but that's not necessarily the case.My main issue with the movie was how exactly did Alicia die? The building was completely intact, and even the kittendog(apparently it's a kitten) survived - so she got done in by looking at it? Even Precia herself survived, and she was right where it happened.
Precia and the rest of the researchers no doubt had a shielded area or safe room in the facility for that kind of emergency. Any facility of that kind should have one.
edit: spent so long on the first part that Kraco beat me to the second part!