A question about common mode voltage protection of a device
The device is capable of measuring 30VDC with respect to it's 0V, probably chassis.
This means that there is no real "common mode" voltage at play here. Unless you're using two inputs as differential, in which case neither of the lines may exceed 30VDC.

I do not see what you're are confused about. The manual is very clear, with pictures how to wire it up, and how not to wire it up.

1) Yes, you should check. But if the source is isolated, it might give ambiguous results, like half mains voltage. If the source is not isolated, and the signals are above 30VDC or 21VAC, additional circuitry might be required.

2) It would protect the logger, but it might damage the source by excess currents. I would assume the logger already has transient protection build-in.

3) Yes there will be ground loops. But the manual already provides a solution for that.