Foreign Earned Income

Your form 2555 could be used as evidence against you to take away your green card or deny your US citizenship application.

Instead of form 2555, use the Foreign Tax Credit (see http://www.irs.gov/taxtopics/tc856.html) which enables you to use the tax paid to the foreign government to cancel most or all of the US taxation of your non-US income.
 
Yes, they can revoke your green card for abandonment of residence even if you have a reentry permit (although the only cases I know of where that happened, the people had a consistent pattern of spending over 10 months per year outside the US, for over 3 years, and had other ties outside the US like employment and/or owning a house abroad).
 
Foreign employment is already a factor that could cause you to lose your green card (together with other facts such as whether you have a house or apartment in the US, whether you have a spouse and/or minor children in the US, the length of your foreign employment, etc.).

If you want to minimize the risk of losing your green card for working abroad, get the reentry permit and DON'T file form 2555 for your taxes. Use other methods to reduce or eliminate the US taxation of your non-US income, such as the foreign tax credit I mentioned above, or the tax treaty (if it exists) between the US and the country you're working in.
 
US citizens and permanent residents are legally required to file US tax returns to report worldwide income, unless their income is low enough that they're exempt from having to file. And taxes must be paid on worldwide income unless eligible for available exemptions/credits/deductions/treaties to cancel out US taxation of the foreign income.

As a permanent resident, failure to a required tax return (especially when abroad for extended periods) is another factor that can be used to revoke your green card or deny citizenship.

Your $10,000 income means you probably have to file (I think the threshold is $9000-something, and your income is above that). Check the 1040 instructions for details.

So if you have to file, use methods other than form 2555 to reduce or eliminate the US taxation.
 
Can I file form 1116 Foreign Tax Credit even if I stayed more than 330 days in the foreign country ?
Can I file form 1116 Foreign Tax Credit without form 2555?

Yes to both.

Apparently you're not very familiar with the rules for the Foreign Tax Credit, so I strongly suggest you find a tax accountant to prepare your return. Now that peak March-April tax season is over, the accountants are less busy and you can probably negotiate with one to prepare your return for under $200, especially if the foreign income and tax credit is the only complication you have. There are some accountants that specialize in tax returns for US citizens and LPRs living/working abroad.
 
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