I don't get how this works for a pendulum (or my ball) starting at 0 radians, becuase then $\theta(t+dt)=0$ which is wrong :(

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There is nothing wrong with it.
If you set $\theta(0)=0$ and you find $\theta(t+dt)=0$ it means you also set $\omega(0)=0$
How can a pendulum move if it at equilibrium position without any initial velocity or external force.

If $\theta(0)=0$, you will need to set $\omega(0)\ne 0$, otherwise the pendulum will not move at all.

$\frac{d^2\theta}{dt^2}=-\frac{g}{R}\sin\theta$ is the angular acceleration at any point.
So you should be able to find linear acceleration $a= R\alpha = R \frac{d^2\theta}{dt^2}$ which is the magnitude of the force. And it's direction is in the tangential direction.

You might be able to  find out each component (x,y component) of the tangential component  if you try to draw it's component in a paper.

I will try to help if you still can not figure it out by yourself. But I will let you try it first.