My natives tongues are Catalan and Spanish, so I'm very used to systems in which vowels are pretty straightforward. I've been learning English for a long, long time (and it's not as straightforward, but not as overwhelming as Irish spelling). When I tried to learn it on my own I was always like: is ea pronounced a, e, or neither? Is aith pronounced ah, ih, a, i...? It was really confusing. I've been reading on the forums that the pronunciation in this course is not very good, but still better than trying to figure it out by myself!!
Yes, they all (including "gold") come from a Proto Indo European word neaning "bright" or "to shine". There are many other PIE languages that have similar words descended from the same source.