. . . the shop (opened by James Booth and taken over by Arthur Simpson in 1909) has long gone.
In this clause, the only verb that has a tense is "has". The three other verbs are non-finite forms: "opened", "taken" and "gone". The traditional name for this non-finite form is past participle. That's a confusing name because the past participle has nothing to do with the past tense.
We can consider "has gone" as a coherent verb phrase in the active voice, present tense, perfect aspect and indicative mode. You may have been taught to call this the present perfect tense. I find it easier to understand tense (past, present, and maybe future) and aspect (simple or indefinite, continuous, and perfect) as separate properties instead of lumping them both under the name tense.
Both "opened by James Booth" and "taken over by Arthur Simpson in 1909" are participial phrases. There are at least two ways of explaining how they work.
The way that I prefer is to say that participial phrases can do the same job that adjectives do. In this case, they directly modify the noun "shop".
The explanation that seems to be more common on this site is to say that they are reduced relative clauses. In this case, there are a number of words missing -- "opened by James Booth" is taken to mean "[ [which/that] [is/was/has been/had been/etc.] ] opened by James Booth".
In the end, the difference between these two explanations is small. If we think of "opened by James Booth" as an adjectival participial phrase, then it has no tense in the same way that the adjective "happy" has no tense. If we think of it as a reduced relative clause, then its tense is unknown because the words that would mark the tense are missing.
The phrase "the shop opened by James Booth" does not stand as an independent clause in this context. That may be hard to see because "opened" is both the past tense form and the perfect aspect form (or past participle form). The participles "taken" and "gone" are easier to recognize because they are distinct from the past tense form "took" and "went".
. . . the shop was opened by Sir Edward Elgar.
This is a past tense construction. Specifically, it is in the passive voice, past tense, indefinite aspect and indicative mode. The verb phrase is "was opened". The finite verb "was" marks the past tense and licenses the passive voice. The participle "opened" fulfills the passive voice license.
If we want to express both the passive voice and the perfect aspect, we would need to use two so-called past participles, one for each purpose. For example:
The shop had been opened.
Here, the "had" marks the past tense and licenses the perfect aspect. The "been" fulfills the perfect aspect license and in turn licenses the passive voice. Finally, the "opened" fulfills the passive voice license.