All income must be reported. 

Which is better to assist with deductions: FilingScchedule E or Schedule C for short-term rental income?  Does this type of income quality for "Pass-through" deductions?

Thanks

Yes, it qualifies for pass through income. You will complete Sch E. See this for more information. 

https://assets.airbnb.com/eyguidance/us.pdf

Is short-term rental income taxed federally along with state taxes?

If you rent out your primary residence or vacation home for 14 days days or less throughout the year you do not have to pay federal taxes on the income. States May have different rules. Because your income isn’t taxable, you also can’t deduct your expenses.

Otherwise you would pay federal and state tax.