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Yes your understanding is correct.

1.  'I have full rental expenses like the tv, bed, furnishing, supplies I purchased for the room and x% expenses like mortgage interest, PMI, depreciation, home insurance, utilities, certain closing costs and real estate taxes where x% is the percentage of the home used for the rental.'
   1. Yes, and you can use the square feet of the extra room if it is strictly for the Airbnb activity and no personal use of items stored there (if you didn't do that already). The calculations are reasonable for accuracy.
   2. No the days the unit was not available cannot be counted because you literally would not rent it during those days.
   3. Answered in number one, the key is that the storage square feet must be for the Airbnb activity only and it must be identifiable as a distinct space for the Airbnb.  This means it could be 50% as you mentioned.
2. It's unclear if you are reporting this on Schedule C for self employment or Schedule E for residential rental.  I would advice you to report it on Schedule E assuming you are not providing amenities substantial services and enter the percentage of expenses, the home asset at the business use percentage and calculate the percentage as you have already done. Then indicate it was rented all year.  You have your records should you need them later. 
   1. Should I report my rental on Schedule E or Schedule C?
      • Schedule E allows passive activity losses against other income if you meet the income levels. Phaseout Rule: The maximum special allowance of $25,000 ($12,500 for married individuals filing separate returns and living apart at all times during the year) is reduced by 50% of the amount of your modified adjusted gross income that’s more than $100,000 ($50,000 if you’re married filing separately). If your modified adjusted gross income is $150,000 or more ($75,000 or more if you’re married filing separately), you generally can’t use the special allowance. This is because the special allowance is reduced to $0 since the modified adjusted gross income is over the $100,000 amount.
      • Schedule C, although you have a loss now, would require self employment tax in any profit year or years.
3. Deductions:
   1. No, the home office must be exclusive use. IRS Publication 587
   2. Closing costs incorporate many items.  See the list below that can be added to the cost of your home, then include that amount with the total cost basis before you enter the depreciation cost basis.  

Government Recording and Transfer Charges 

• Recording fees
• Title Charges
• Lenders Title Policy
• Settlement or Closing Fee
• MLC  - Assuming it means Municipal Lean Certificate
• Title Exam
• Owners title Insurance

You can include these closing costs and add them to the cost basis of the property as noted above.