The plural of "новость" is "новости". You choose whether to use the plural or singular depending on the context. For example, for "I am watching the news" you'd say "Я смотрю новости" and "I have a piece of good news for you" is "У меня для вас хорошая новость". If you're just talking about news in general, better use the plural, but if you're talking about some specific piece of news, then use the singular. Hope this helps :)
They are almost synonyms. Известие sounds bookish, some new message about someone or something. There is a Soviet, and now Russian, newspaper called "Известия". Another synonym is "весть", where you can see the same root - "-вест/вещ-". Compare with "вещание" - "broadcasting", "извещение" - "notification". We use новость/новости (singular/plural) in 90+% cases. Btw, now we have two news TV programs - "Новости" and "Вести" - on two main TV channels of Russia.