How long will it be until the nearby groups of galaxies are receding at speeds faster than light? And subsequently how long will it be until we can never see them again?
This will take about 2 trillion years.

Given everything we know now, it's not too hard to predict the eventual fate of the universe. Of course there may be some changes as our knowledge advances, but I think the general course of events will occur as we expect them to. Based on our current knowledge, if you run through the math, you find that after about 2 trillion years from now, the expansion of the universe will have made it so that all by the closest galaxies will no longer be visible to us. You do ask two separate questions, but they're more or less the same question. They might not occur precisely at the same time, but predictions of the future aren't precise enough to distinguish such a small time difference.

By the way, you can read more about the future of the universe on Wikipedia, and specifically this section as it relates to your question.