We can understand both sentence, and they are really good, but at least in Colombia we usually say:
"Le di una lavada al carro".
The female article (una) and to get the concordance between article and verb we change "lavado" for "lavada".
"I kissed her or I gave her a kiss". In this case, your sentence is completly correct and in spanish we use the same structure:
"La besé". "Le di un beso (a ella)". [no es necesario usar el pronombre si en el contexto se sabe a quién se refiere].