sat writing blue book practice question?

Test Preparation
1

I just stumbled upon this question in the writing section of the practice test in the blue book.

Neither Ms. Perez nor Ms. Tanaka (believes) that watching as much television as (her) son Sam does (will lead) to anything productive. (No error)

I know that the correct answer is to fix her, but I thought that when you use neither, you follow up with a singular verb? So wouldn’t it be Neither Ms. Perez nor Ms. Tanaka believe that watching…?

I also have a question on this one

An amateur potter (herself), the accountant offered (to help) the artist with his business accounts, complicated (as they were) (by) his unusual system of record keeping. (No error)

I thought you can’t use “they” to replace things that aren’t humans and it is vague as in what “they” refers to?

2

Believes is a sing verb. When you use neither, the verb agrees with the second subject.

3

Believes is correct, and @Argentina2017 is right that it’s singular. The error is “her” because it’s ambiguous.