Learn English – Is it common to use “perverted” (as in a pervert) as an adjective

Governor (dated 13th century) comes from gouernour (“personal keeper, protector, guide”), from the Old French governeor (11th century), itself form the Latin gubernator. The same can be said from other compounds with this root: govern comes from Old French governer, etc.

Gubernatorial, on the other hand, is more recent (dated 1734 by Etymonline) and was formed directly from the Latin root gubernator, hence the difference.

On the reason why thoses two didn't merge (or haven't merge yet, as they well may in the future), it's hard to say. It's worth noting that gubernator has seen a rare but continued used since the 15th century (1,2), and governatorial shows some increase in usage (though still rare) for the last century (3).

It depends what you mean by ‘common’. The Corpus of Contemporary American English has 10 records for to grocery shop, and the Oxford English Dictionary has this citation 1979 citation from the Arizona Daily Star:

Volunteers are needed to grocery shop for elderly shut-ins.

There are no records for the string in the British National Corpus.

If you say any of the sentences in your final paragraph, it is by no means certain that you will be understood. Barber shop, as a verb, sounds as if you’re shopping for barbers, an unlikely activity. The verb grocery shop is established, to the limited extent that it is, because shopping for groceries is fairly common. Language exists to meet a need, and there would seem to be even less of a need for a special verb for shopping for golf clubs than there is for shopping for groceries.