I think I understand, thank you.

In regards to my einstein or tensor question, I could be wrong but I think they are the same thing. We use tensors precisely for the reason that they do what the einstien postulate wants,that is the equations take the same form in a any lorentz frame. Is this correct?

Yes, I think I understand. If we do a lorentz transform and require that the equation remain the same(not sure if this is an einstein postulate or a tensor thing) we have $\frac{\partial}{\partial x^{'\alpha}} F^{' \alpha \beta} = -J^{' \beta}$. So that $\Lambda_{\alpha}^{\gamma} \frac{\partial}{\partial x^{\gamma}} F^{' \alpha \beta} = \Lambda^{\beta}_{\delta}J^{\delta}$ iff $F^{' \alpha \beta} = \Lambda^{\alpha}_{\gamma} \Lambda^{\beta}_{\delta} F^{\gamma \delta}$. Is this the line of reasoning?

So a more hands on work calculation could consist of giving multiple forces, finding the net force, applying newtons laws to find the trajectory of the particle then calculating the work done by one of these forces or the net force. Is this correct?

Thank you for you answer, in regards to your last paragraph have I understood this right? There may be multiple forces acting to give us the specific curve given but we are calculating the work done by one specific force along this curve?

Am I correcet in saying that when we simplying add velocities like that we assume the acceleration is instant then?