Well, first, this is an assumption on Cheng's behalf. There is a lot of inteferrence and he's receiving no reply. Second... he doesn't want to upsent Lena. Third, he's using a base station transmitter. It has more power and can reach further than an onboard radio can. It can collect weaker signals, but it would be like boosting an already distorted signal. It sends the transmission at high power while it is pure and undistorted, but it has to listen to it from a signal that has been heavily distorted at the source.
It is extra special, for its size.
The storm has likely destroyed their home. They will get to return to their island, if it even still exists (it itself might have been destroyed), but their home would be destroyed.
Family. I assume she means you haven't lost your family.
It's a handle. Likely for a hatch (door).
The storm brought it to the other place.
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Also, I apologise profusely for placing this torment on you.