Pretension is high on the menu in "All Tomorrow's Parties," a joyless tranche of post-apocalyptic dystopia set in continental East Asia that's headed nowhere except arty fests and digital friendly ...
Some great Gatsby quotes about parties include "I like large parties. Theyre so intimate. At small parties there isnt any privacy" and "In his blue gardens men and girls came and went like moths ...
The difference lies in whether both parties can report or not. (a) implies that only one party will report (although "either party shall report to us the new discovery" sounds more natural and is the one that I have heard used, whereas I have never heard the addition of "of both" to the statement). (b) implies the possibility of both parties reporting the discovery although it could still be one.
The 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language, would consider words like yesterday, today, tonight, and tomorrow as pronouns (specifically, deictic temporal pronouns). Related info is in CGEL pages 429, 564-5.
The contraction "tomorrow's" is used to mean "tomorrow is" all the time. Just search for "tomorrow's going to" to find all manner of examples.
Tomorrow morning is idiomatic English, tomorrow's morning isn't. Night sleep doesn't mean anything in particular - you have had a 'good night's sleep' if you slept well all the previous night. So there is no pattern to whether or not you use an apostrophe.
Is there such an expression in English that means "not today, then tomorrow" ? I wonder whether the Russian phrase "не сегодня, так завтра" (which translates exactly so and means "soon, eventually") has an equivalent in English.