Yes, United States citizens are liable for taxation on their worldwide income (unless there is a tax treaty between the United States and the other country in question).
Only over some threshold (iirc, though it has been some time, around 80k USD equivalent). So maybe yes for someone with a comparatively high income, but not so much a worry for a reasonably large segment of the population. Naturally if this happens to apply to anyone reading I would urge consulting a professional for current advice. ;)