Reviewing the subject-verb and pronoun-antecedent agreement rules

[AExAVF]

I am currently reviewing for the government service licensure examination, and right now I'm refreshing myself on the most basic of English grammar rules, namely the subject-verb agreement.  In addition, there is also the sometimes confusing pronoun-antecedent agreement rule.

Here are some sample sentences:

Each of the contestants was given a room for themselves.

Each contestant was given a room for herself.

In the first sentence, the pronoun themselves refers to its antecedent contestants, while in the second sentence, herself refers to contestant.  Here is a common error:

Each of the contestants was given a room for herself. 

Without the phrase of the contestants, the sentence would be correct, e.g. the second sample sentence, or also read as follows:

Each was given a room for herself.

In this case, the pronoun herself refers to each or each beauty contestant, which is singular.  The modifying phrase of the changes the antecedent, making it plural, which in turn changes the pronoun from herself to themselves.

Here are some more sentences:

Each soldier listened attentively to the captain and then reached for their rifles.

In this sentence, the pronoun their refers to the antecedent rifles, notwithstanding that each soldier is singular.

I've chosen these sentences because this is where I had my share of errors during our diagnostic and achievement tests in English, so I thought I'd post them here for any clarifications.

[AureliaeLacrimae]

Although, one valid point here is: how do you know all contestants are women? When it comes to matching "each" with a reflexive pronoun/anaphora, the textbook usually opts for masculine form "himself". It's the accepted form in the standard English. Only lately did the trend of choosing feminine form appear. I really don't understand why all the fuss. It only makes the matters more complicated.

It may be clumsy using himself/herself in formal style (although I'd seen this in sentences and it looks awful, it completely ruins the rhythm of the sentence), so I'd always opt for plural:

All - themselves

There's no mistake there. And no one will argue.

Same is with "Every student has handed in his assignment". -how do you know they're all men? perhaps they're all women? or mostly women?

This is why many grammar books suggest: "All students have handed in their assignments."

Although, when it comes to mixed gender (3 fem, 2 masc. nouns, for example), many languages would still opt for masc. pronoun form.

I had encountered a similar sentence to "Each contestant was given a room for herself." I think I had a version with "his own"? I can't remember. Still, it's better to use plural "their own".