for "regressive" and "progressive" to mean something useful, you need to take into account what the tax proceeds are used for. if a mildly regressive tax is used exclusively to fund healthcare for the poor, it's probably not regressive in the end. if a highly progressive tax is used exclusively to finance wars for the elite, it is probably not progressive in whole.

If imposed at a blanket level, then yes. But zero-rating some items (e.g. food, housing) and higher-rating others (yachts, private jets, ...) can address that to a certain extent.

Or what Canada does, which is rebate over the year based on your income level and assumed consumption.

The are usually offset by either multiple consumption tax rates (luxury vs necessary goods like food, toilet paper, etc) or income tax deductions in the lower brackets. Either by excluding taxes at lower income or by subsidies for those groups.

I favor a minimum income and/or earned income tax credit to offset.