“Быть” with tenses, gender, number but in affirmative sentences

Question

A homework question, exactly quoted,

В этот период у нас было много неожиданных трудностей.

but in reviewing my previous question, When to use 'не было' and 'не будет' regardless of person, gender, or number I am reassured that, without negation, the verb быть needs to agree in gender and number with the noun.

The last word, the noun, is feminine, but plural.

• I believe that without много, the trailing adjective and noun would be nominative plural.

  Correct?

  I often think of verbs, prepositions, etc. affecting other words 'downstream', and yet it seems много affects the verb быть.

  Is this a fair assessment?

• So should the sentence actually use были?

Answer 1

1. Indeed были can be used without много, which ultimately changes the meaning of the sentence

В этот период у нас были неожиданные трудности. (no info on their volume)

2. No. In the original sentence the subject is not неожиданные трудности but много (неожиданных трудностей), and naturally the predicate быть conforms to the properties of the subject. It's only natural for a subject to affect a predicate.

Subject can be either noun, pronoun, numeral or null. Here we have it as a numerical pronoun.

Answer 2

In case there is an adverb describing quality (много, несколько, немного etc.) or a numerical, the verb быть must be in neutral singular, i. e. в автобусе было двадцать человек, у нас было несколько домов, в зоопарке было много животных. Same with сколько:

• Сколько котов было у вас?
• У меня было пять котов.