@abhinavgulechha
From your points:
1. while the term "proportionate " is correct but it is used as a mechanism to identity/compute the US tax on that doubly taxed income. This is because , while the treaty generally requires US to recognize / credit taxes paid to a foreign country, it generally cannot allow more credit than US taxes on the same income. Thus the US recognizes the full foreign taxes paid ( dollar for dollar ) but the allowable credit for the US tax year is the lesser of the amount paid to the foreign taxing authority and the US tax on the same income.
Note that the doubly taxed "foreign income" is generally the lesser of the foreign source in come per US laws and the foreign source income per the "other contracting" country. This can get quite messy / involved because while the "gross" income may be the same the adjustments/ deductions to it are computed per the laws of US and the pother country ( per the saving clause ). A classic example of this is for foreign source rental income --- everybody agrees on the gross rent amount, but the allowable deductions including depreciation, amortization etc. vary from country to country. Therefore , one needs to keep in mind what one is trying to achieve --- the doubly taxed income ( i.e. that portion of the foreign source & gross income that is being "taxed " by both countries ( mitigation / avoidance of double taxation clause ).
Your points 2 and 3 are things to be aware of --- residency per the state laws and absent direct State to country ( e.g. Canada & NYS, Canada & MI ), US states generally do not recognize US and another country tax treaty conventions/ articles.
