as far as i know the speed of light is constant. in other words, it cannot go faster than 186,000 mps. as far as your questions about the earth appearing to be motionless, i believe the opposite might be true. the ship would appear to be stationary and the earth would be spinning like a top. it has to do with time dilation, i think. would your ship heat up? i don't know, but if you were to suddenly hit a speck of dust or something, your ship would be destroyed. i hope this answer helps you.
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