Learn Russian: Это был живой и весёлый вечер.

When это acts as a placeholder meaning "it" or "this", the past tense verb agrees with the noun it points to. Because вечер (evening) is a masculine noun, the verb becomes the masculine был. If you were introducing a neuter noun like утро (morning), the verb would agree with that neuter noun: Это было утро.

I learned that живой means "alive". Is it common to use it for inanimate concepts like an evening?

Yes! Just like the English word "lively", the adjective живой is frequently used figuratively to describe events, conversations, or places that are vibrant, active, and full of energy.

Could I use the adverb весело instead of the adjective весёлый in this sentence?

No, because we are directly modifying a noun here. We need the masculine adjective весёлый to describe the masculine noun вечер (a cheerful evening). You would use the adverb весело to describe a general state or an action, such as Вчера нам было весело (We had fun yesterday).