On Generalised Danielewski Surfaces over fields of arbitrary characteristic

In this paper we study exponential maps (${\mathbb{G}}_a$-actions) on the family of affine two dimensional surfaces of the form $f(x)y=\phi (x,z)$ over arbitrary fields, describe the Makar-Limanov invariant and Derksen invariant of these surfaces, give a complete characterization of isomorphisms between such surfaces and display a subfamily which provides counterexamples to the cancellation problem.