Are all mobile devices capable of using their respective digital wallets? (i.e. Can all iPhones use Apple Pay?)

No. Older phones are not compatible. Below are general rules of thumb to use:

iPhones have to be iPhone 6 or newer.
Samsung phones have to be Galaxy 6s or newer.
Android Pay is available on all non-rooted Android devices (KitKat 4.4+).
See your device manufacturer for more specific details.