Can FOREIGN TAX WITHHELD on a stock one owns be claimed or not be charged in the first place? Anything one can do, or this is just an expense one has to live with if you want to own that stock?

You can claim a foreign tax credit on foreigntaxces apid to foreign taxing authority(ies); Your foreign tax credit cannot be more than your total U.S. tax liability multiplied by a fraction. The numerator of the fraction is your taxable income from sources outside the US.you can claim it on form 1116 as either itemized deduction on SCh A of 1040 line 8, I guess or as a foreign tax credit on your 1040 line 48.
On the contrary, You'll report the stock sales just like you'd report the sale of US stocks in the US. when Americans buy stocks from a company based overseas, any capital gains are subject to U.S. tax, then,as said above if you alos need to pay tax to the foreign taxing authority then you may claim the foreign taxon your US return since you are not subject to double taxation.

My query about foreign tax is related to foreign tax charged when a dividend is paid by a company and that company is of foreign origin. For example, Mittal Steel is based in Luxembuorg and when dividend on this stock is received a foreign tax is withheld. Below is reply received from TD Ameritrade:

"Foreign tax is generally applicable when a dividend is paid on a foreign security. Any clients that hold a foreign security in their accounts will be subject to the tax rate of the country the security originates from. You may want to speak with a tax advisor for assistance in claiming any foreign tax withheld in an IRA. They should have information regarding this."

How can I claim such foreign tax withheld when dividend is paid in an IRA or a regular investment account?

My query about foreign tax is related to foreign tax charged when a dividend is paid by a company and that company is of foreign origin. For example, Mittal Steel is based in Luxembuorg and when dividend on this stock is received a foreign tax is withheld. Below is reply received from TD Ameritrade:

"Foreign tax is generally applicable when a dividend is paid on a foreign security. Any clients that hold a foreign security in their accounts will be subject to the tax rate of the country the security originates from. You may want to speak with a tax advisor for assistance in claiming any foreign tax withheld in an IRA. They should have information regarding this."

How can I claim such foreign tax withheld when dividend is paid in an IRA or a regular investment account?

As said previously, at least a portion of foreign dividend withholding tax can be recovered. To avoid double taxation, the IRS allows taxpayers to claim either a deduction or a credit on their tax returns to make up for some of their foreign taxes. shares held in IRAs are not eligible for this tax recovery and investors should consider this when deciding what to put in their IRA. One of the best ways to avoid dividend withholding tax is to invest in countries without such a tax. some countries , india or singapore UK,don't withhold foreign investors' dividends. however, there is always a risk that these tax policies could change as these countries look for additional revenue but for now they allow U.S. residents to easily avoid dividend withholding taxes.Unless it is US tax withheld /charged when a dividend paid by a foreign firm, US tax law is beyond this situation.
so once the foreign firm charges tax on the portfolio income, you , I guess, may claim the tax paid to foreign portfolio income on your return.