After you file

Yes, let's take each question  one at a time.

1. You are reporting your wife's foreign income. You may be trying to see if you can receive a foreign income exclusion for her but this is only for US Citizens that are residing in a foreign country.  To qualify, they need to either be eligible under the physical presence test or bonafide residence test. Your wife is this case would not be eligible to exclude her foreign income because she is not a US Citizen or Resident Alien. She is neither of these but if you are making the election to choose her as a Resident Alien for tax reporting purposes only and allow you to Married Filing joint.
2. You are eligible for the Foreign Tax Credit but you are unable to use it this year. It then will be carried forward to the next ten years to help offset future foreign income. The foreign tax credit is non refundable credit that helps reduce tax liability  to zero. if your tax liability was already zero, then none or little of the credit is applied thus will carryover for the next ten years.
3. If you are referring to US taxes paid through withholdings, you will be given credit for those tax payments.  If it is Foreign Taxes, then from what you tell me, the credit is applied but not being able to be used because of limited tax liability to apply the credit.

@vsundar