Predicting acceleration along curve based on degrees

What you're looking for is no easy task.

For example you ask:

For example, when it hits the curve, it has to slow down. When it hits the hard 90 degree angle, it has to almost come to a stop, but then accelerates out.

For argument's sake assume the car enters a curve that is part of a perfect circle, then in order to stay on the curve a centripetal force $mathbf{F_c}$ must act on the car:

$$|mathbf{F_c}|=frac{m|mathbf{v}|^2}{mathbf{r}}$$

where $m$ is the mass of the car, $mathbf{v}$ is the tangential velocity vector and $mathbf{r}$ the radius vector.

For an unbanked turn, $mathbf{F_c}$ must be provided by friction with the road surface:

$$|mathbf{F_c}|=m|mathbf{g}|mu$$

with $mu$ the friction coefficient.

So that:

$$|mathbf{g}|mu=frac{|mathbf{v}|^2}{mathbf{r}}$$

from which the maximum speed $|mathbf{v}|$ for that turn can be calculated.

But for real tracks, like the one you depict, the turns don't have a constant radius. Instead the concept of curvature could be used.

Probably the safest way to navigate a given turn is to calculate a maximum $mathbf{v}$ for the point of minimum curvature in the whole bend, then take the whole turn at that velocity.

For example for the left, $180^{circ}$ turn, curvature is clearly smallest at the 'top'. Note also that "$180^{circ}$" does not help us calculate the forces acting on the car, in physics that number has no real use.

For $90^{circ}$ turns the curvature becomes momentarily $0$ and the car must momentarily stop ($mathbf{v}=0$)

To calculate the accelerations/decelerations in between turns, you have to think like a racing driver: accelerating from one bend, then decelerating again to prepare for the next bend.

I'm trying to do a really basic simulation of a body (eg car) moving along the line and keep it feeling natural with acceleration and deceleration.

I don't think there's a simple algorithm that would allow to do this. Everything depends on maximum velocity of the car, its power and its maximum braking force.