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How would it impact a solar system if one of these relativistic stars got too close? Any chance it could pick up a few planets, or would they mostly be flung into space?

Along that point, what does the heliosphere of such a star look like - a giant comet?

Lastly, were a life-bearing planet sent into space this way have any chance of maintaining that life without a parent star to heat and magnetically shield it?

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Chances are nothing would happen as space is vast, but if it did get too close, it would be going way faster than anything around it, as it would be on a different plane. It would just scanner whatever is nearby like a big boat in a small pond.

The heliosphere would look normal because there would be no drag on it. A comet has a tail because the sun is both melting and pushing material away from it.

Lastly, we could probably heat our homes with the core of the planet for a little while, but everything would be dead within a few years. I think the Twilight Zone covered this scenario in an episode! In it the Earth started moving away from the sun for no good reason.

See “A Pail of Air" by Fritz Leiber: https://en.m.wikipedia.org/wiki/A_Pail_of_Air

A great story. Also, for some reason, it shook me deeply. I still feel dread when I think of it. Such hopeless scenario for humanity.

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