I started a business in 2013 (a New York LLC where I am the only owner and employee) and did not make a profit. Do I need to file income taxes next month? I would be reporting an income of $0. Do I need to file a P&L statement showing that I did not make a profit?

#1;I guess so; Even if you don’t have to file, you may want to:aslongas you have Federal Income Tax Withheld You should file to get money back if Federal Income Tax was withheld from your pay, you made estimated tax payments, or had a prior year overpayment applied to this year’s tax. Please read below.

#2;Yes; to claim your NOL; you may use either Form 1045 or Form 1040X to claim an NOL refund.Form 1045:You can use Form 1045 to apply an NOL to all carryback years.You'll get a faster refund using Form 1045 (usually within 90 days).
You must file Form 1045 no later than one year after the NOL year;sume that you have an NOL for 2013 ,the NOL year.
And you're a calendar year taxpayer ,Jan. 1 through Dec 31, then you must file Form 1045 no later than Dec. 31, 2014. Do not file Form 1045 with your original Form 1040. File Form 1045 separately and attach it to a copy of Form 1040. Instead of Form 1045, you can use Form 1040X to file for a refund. If you choose to use Form 1040X, you must use a separate Form 1040X to amend each carryback year to which you apply an NOL.It takes longer to get a refund than if you use Form 1045.One advantage is, you have more time to file Form 1040X than Form 1045.You must file Form 1040X within 3 years after the due date including extensions for filing Form 1040 for the NOL year.Assume that you have an NOL for 2013, you're a calendar year taxpayer. And your Form 1040 is due Apr.15, 2014, then, you carry the NOL back to 2011 ,two years prior to the NOL year 2012. You must file Form 1040X no later than Apr. 15, 2017 ,the third year after the April 15, 2014 due date, plus extensionsYou report your NOL on 1040 line 21 in neg. number..you need to Determine if you want to carry back the NOL to the prior 2 years or only to future years for 20 years.So you may carry forward to future years any NOL not used in years prior to the loss year and deduct the amount as a negative number on the Other Income line of Form 1040 I mena line 21 of 1040. Attach a statement which explains how you computed the NOL carry forward.