Learn Spanish (Latin America): El arquitecto tuvo mucho éxito en su época. - The architect had a lot of success in his era.

The preterite tuvo looks at his career or a specific era as a completed chapter. It implies that this period has ended. If we used the imperfect tenía, it would sound like an ongoing background description in a story (for example, 'He was having a lot of success when something else happened').

Since we are learning the passive voice, could we say Mucho éxito fue tenido por el arquitecto?

No, that sounds very unnatural. The analytic passive voice (fue + past participle + por) is mainly used for direct actions performed on a subject, like a building being designed. We generally do not use the passive voice for verbs of state or possession like tener (to have).

Why is it mucho éxito and not muy éxito?

Éxito (success) is a noun, so it takes the adjective mucho (much / a lot of) to describe its quantity. Muy (very) is only used before adjectives and adverbs, so you would only use it if you changed the sentence to say he was muy exitoso (very successful).

Does época translate directly to the English word 'epoch'?

They are related, but época is used much more broadly in everyday Spanish than 'epoch' is in English. It is the standard, normal word for 'time,' 'era,' or 'period' when talking about someone's life, a historical stretch, or even a time of year.