In the sentence “I went jogging” am I correct in thinking “went” is the verb? And jogging a gerund?
In the sentence “David jogs for a mile every day” Jogs is the verb?
In the sentence “David had jogged yesterday” Had and jogged are both verbs
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Your examples, rearranged to put the two easier ones first:
2 "David jogs for a mile every day”
Yes, "jogs" is the verb.
3 “David had jogged yesterday”
"had jogged" is the verb "jog", conjugated as past perfect.
The verb "had" is an auxiliary, and it doesn't have a separate meaning; it just marks the past perfect.
1 “I went jogging”
You can consider "went jogging" a verb.
The following text calls this usage one example, among others, of "verb + participle":
Oxford Guide to English Grammar, John Eastman
Oxford "go/come + participle"
138 Verb + participle
(2) We use go/come + active participle to talk about some activities away from the home, especially leisure activities.
I'd love to go swimming.
We went riding yesterday.
Come cycling with us.
Mac goes jogging every morning.
(The entire quotation is not available online).
This text calls it "verb + -ing":
Collins Cobuild "v -ing"
I.4 The 'go riding' group
These verbs are concerned with taking part in an activity, often shopping or a leisure activity.
The next afternoon Amy went riding with Gerald.
It may be worth pointing out that "verb + participle" or "verb + ing" forms may vary significantly. Compare these sentences:
I went running.
The main meaning is in "running", and "went" just means that I left home to do it.
I came running.
In that sentence, the main meaning is in "came", and "running" is more of an adverb. (For example, "When she called, I came running.")
 I went jogging.
 David jogs for a mile every day.
 David had jogged yesterday.
In  "jogging" is undoubtedly a verb. The verb "go" is called a catenative verb because it takes non-finite gerund-participial clauses as complement. Here "went" has the clause "jogging" as complement. We know that "jogging" can't be a noun (your gerund) since "go" is intransitive, i.e. it's not possible to replace "jogging" with a 'real' noun (we can't say *I went shops" or *"I went Paris") etc.
In  "jogs" is clearly a verb, and in  "had jogged" is a perfect construction with the auxiliary verb "had" and the past participle verb "jogged".