Some Answers

I posed some of my questions to my astronomy professor and here are his responses.

1. If the universe is eternally expanding, is it possible to be completely motionless?

Motionlessness is just as relative as motion is. One object can neither be motionless nor have an absolute velocity-- motion is a relationship between at least two objects. In relativity, anyway-- who knows how that view might change. So the expansion of the universe is a statement about the increasing distances of things that are very far from us-- but something very nearby could have no motion relative to us. However, complete motionlessness is an impossible limit-- at some level there would always have to be some motion, but we might not be able to detect it with a particular instrument.

2. If I could accelerate the earth until the entire thing was moving at the speed of light would time stop on the earth? Would people on earth age or be able to procreate? Would mechanical objects such as watches stop? Would people not age but still die because they wouldn't be able to digest/cook food/ have natural body processes?

No, there is no speed, relative to something else, that would make Earth's time appear to stop-- because we would always think it was the other thing whose time had stopped. They would think our time stopped, but we wouldn't think that. However, all the other things that were moving at the speed of light, which in your situation would be the whole rest of the universe, would be so length contracted in the direction of the motion that the whole universe would seem to be right at our doorstep and it would have to be infinite for us to not run into the end of it very quickly. Basically, it is an impossible scenario to be moving at the speed of light, for anything but light.

3.If everything is accelerating away from everything else at increasing speeds could it be visually represented as dots (representing objects in space planets etc.) inside of bubbles and the bubbles continually get larger pressing every surrounding bubble away from them and being pressed away as well?

Yes, bubbles or balloons are a commonly used analogy. They work for a two-dimensional universe that closes back on itself, but ours has three spatial dimensions and probably does not close back on itself, so the analogy can't be taken too seriously, but it's not too bad.