Space time is not moving. There is just more space being created, and it gives the illusion of moving.
Ill use an analogy with a tennis ball.
If i stand 1 meter away from the ball, and then it increases to 2m, it will appear to me as if that thing has moved away from me.
But whats actually happened, is that neither me or the ball has moved. 1m of space has popped into existance between us.
The rule of light speed is that no information can travel faster than light. But the universe expanding does not transmit information. As in, we cant use this expansion to send stuff to other places faster than light.
If i jumped away from the earth, i would not speed away from the earth at lightspeed at some point, while at the same time approaching another galaxy at lightspeed. I would instead be moving away from both. Since there is space being created both inbetween me and the earth, but also inbetween me and the other galaxy i jumped toward.
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