היא שואלת אם יש לי איפה לשמור את התיקייה הזאת, ואני אומרת שכן.

Often, yes, Hebrew can leave subject pronouns out — but in the present tense, the verb usually shows only gender and number, not person.

So שואלת could mean:

• I ask (female speaker)
• you ask (female singular)
• she asks

And אומרת could mean:

• I say (female speaker)
• you say (female singular)
• she says

Because of that, pronouns like היא and אני are often used in the present tense to make the subject clear.

Both are present tense, feminine singular forms.

• היא שואלת = she asks / she is asking
• אני אומרת = I say / I am saying said by a female speaker

If the speaker were male, it would be:

• ואני אומר = and I say

If the first subject were masculine:

• הוא שואל = he asks

So the endings here are showing feminine singular.