once you've applied for a i-131 permit,when can you leave the country?

Answer 1

After you get it back and see that it's approved.

Answer 2

Depending on how you are using the I-131 Travel Document, then yes.

If you are applying for an I-131 as an Advanced Parolee, meaning you have an application for Permanent Residency, etc. pending, then you have to wait on an approval to be heard and then actually receive the document (which is very similar to a passport).

If you are applying for an I-131 as a simple Travel Document, used in lieu of a Passport from your home country, you have to wait for the approval/document itself before you can travel because it substitutes as your passport.

If you are applying for a Travel Document in addition to your passport, or because you think you may be outside the country for more than 1 year and you do not want to lose permanent residency, then as long as you have your valid passport then you can travel and have the document sent to you overseas.

If you even think there could be a possibility of your stay lasting over one year, you should apply for a Travel Document because once you leave you cannot apply for it overseas... It is valid for two years and you do have to return to the United States in order to process a new document.

If you need anymore assistance, feel free to contact USCIS' National Customer Service line at 1-800-375-5283. Representatives are available 8AM-6PM, M-F to take your calls all throughout the United States. There is a bit of a hold due to very high call volumes, but you will be provided with consistent and appropriate information... The website is also http://www.uscis.gov for any additional information.