Say I have a lamp on a car $M$ in the middle of $A/B$, who are both $c$ distance away from $C$. (so it takes light 1 second to travel to both $A$ or $B$ from $M$). Now the car starts traveling to $B$ with lamp turned on, with speed of $1 m/s$ (so very small comparing to the speed of light). Who among $A$,$B$ would observe the light earlier?

My understanding of the special relativity is that we have to use https://en.wikipedia.org/wiki/Velocity-addition_formula to compute the relative speed. The the velocity of the light to $A$ is $\frac{c-1}{1-(c/c^2)} = c$ where the velocity of the light to $B$ is also $\frac{c+1}{1+c/c^2} = c$. so $A$ and $B$ should observe the light at the same time.

Is my understanding correct?

If my understanding is correct, say the car is moving with the speed of light. Then the above relative velocity to $A$ is $0/0$. How do we answer that question?

Say I have a lamp on a car $M$ in the middle of $A$ and $B$, who are both $c$ distance away from $C$. (so it takes light 1 second to travel to both $A$ or $B$ from $M$). Now the car starts traveling to $B$ with lamp turned on, with speed of $1\ \mathrm{m}/\mathrm{s}$ (so very small comparing to the speed of light). Who among $A$ and $B$ would observe the light earlier?

My understanding of the special relativity is that we have to use https://en.wikipedia.org/wiki/Velocity-addition_formula to compute the relative speed. The the velocity of the light to $A$ is $\frac{c-1}{1-(c/c^2)} = c$ where the velocity of the light to $B$ is also $\frac{c+1}{1+c/c^2} = c$. so $A$ and $B$ should observe the light at the same time.

Is my understanding correct?

If my understanding is correct, say the car is moving with the speed of light. Then the above relative velocity to $A$ is $0/0$. How do we answer that question?