"I eat although I do not cook."
Translation:Εγώ τρώω αν και δεν μαγειρεύω.
There are some differences:
(In general, one can either say "I eat although I do not cook" (no comma) -or- "Although I do not cook, I eat" (comma needed). With "however", a comma is always needed: "I eat, however I do not cook".)
As far as the suggestion in discussion is concerned, there's a sense of "concession" when using "although" ("In spite of the fact that I do not cook, I eat"), as opposed to "however", which means "but/nevertheless" and is used as a way of transition between the two ideas/facts that the phrases convey (namely, the two clauses).