Linear regression assumptions
These are not (direct) assumptions for linear regression.
But rather for OLS-Ordinary Least Squares which is widely used to estimate the parameter of a linear regression model. OLS estimators minimize the sum of the squared errors (a difference between observed values and predicted values). 

In order to guarantee finding best possible parameters, we make these assumptions (as with every optimisation)

But just because they are not present that does not mean that linear regression wont work.

Regarding your other models: If they use the same optimisation, than they have same assumptions.