Is my iPhone 7 that was bought in Japan compatible with Verizon neywork and H2O wireless network?
Yes. The A1660 (which supports both GSM and CDMA) is identical in terms of cellular capabilities. This is the phone you'd get under a Verizon contract, or if you just buy one without a contract. The A1779 differs only in that it includes contactless NFC for use in Japan.

All models of the iPhone 7 support GSM, so H20 is no problem.