Well, about passato remoto let's say you will hardly hear it or need to use it during a conversation. A broad knowledge of its forms, at least to be able to recognize it, would be recommended, especially if you want to read history books or literature. Another interesting fact is, talking about passato remoto, the difference between north and south Italy. While in the North it has been completely eclipsed by passato prossimo, in the South is still pretty much alive. Not only, in southern dialects (Sicilian, for instance) it replaces passato prossimo in everyday talking about past events, also recent ones.

Instead, about congiuntivo you do not have to worry yet. It is true that in everyday spoken language it is often replaced by indicativo, but still it is considered a serious mistake.

Interesting to get your perspective of the current state of the languages evolution. I was wondering why I hadn't heard the passato remoto used much in conversation. I am glad that its being eclipsed by the passato prossimo as the passato remoto was a hard one to place as an English speaker learning Italian. Given its decline I guess I can take a pass on spending time learning it? Not good news to hear about the congiuntivo being neglected these days, I really like how it sounds, nice and flowy.