It means they were trying to get to shelter before it started raining.Question one:
Here is one line as follow, and i feel strange why author used "beat":
"We started home, trying to beat the storm. The lightning was near
(Instead of "I feel strange why author used beat" say, "I wonder why the author used beat."
I can't answer your other questions without more--probably considerably more context. The phrases are quite unusual.
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