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Some money would be saved by eliminating the current welfare system and replacing it with UBI.

Most suggestions involve increased taxes.

Yes, although generally up to at least mid middle class, the basic income would offset the increased taxes, so you would end up with at least as much take-home. High-income earners would most likely end up paying more though. (I would argue that the societal benefits would be well worth it.)

Regarding 1, I'm not 100% clear on what you mean.

Typically the money would not itself be taxed. It would offset taxes and, for those making enough money, could take the form of a tax credit.

Hopefully that covers your question.