Can I also set up a second watching wallet on another laptop?
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If I do create another watching wallet, will the 2 watchers keep in step in some way?
You can set up any type of wallet on as many devices as you like, whether it's a watch-only or a standard wallet. Each specific wallet synchronizes with the blockchain every time the file is opened on it's associated device. Like EFTbitcoin said, only the transaction history is synchronized. Labels and frozen addresses are not synchronized between devices.
Electrum for android is very convenient for watch only wallets. I also have a hot wallet set up on my phone and two computers.