What do these prepositions emphasize?
What do the prepositions of "Bis ins neue Jahr," and "Bis zum neuen Jahr," trying to emphasize?
Do you know the difference between 'Etage' and 'Stock'?
There is no difference between Etage and Stock if you use it like in the sentence "Er lebt im fünften Stock/in der fünften Etage" = "He lives on the fifth floor". In this case they are synonymous. (Another synonym would be "Geschoss", for example: Erdgeschoss = ground floor). Stock can also mean different things though, depending on the context, a Stock can be a cane. (Just like Geschoss can mean a canon ball or a bullet or a stone or something else that you might shoot).
The difference between "in" and "zu" in your first question is kind of subtle imo. My interpretation of the first thing would be that something lasts into the new year, as in "Obamas Präsidentschaft dauert bis ins neue Jahr" = "Obama's presidency lasts into the new year" (until 20th January or somewhere around that). The other one I'm actually not sure how to interpret. Maybe if something won't happen until next year, similar to the expression "bis zum nächsten Mal" = "till next time". The more I think about it, "bis zum neuen Jahr" sounds kind of weird, maybe you might say "bis im neuen Jahr". This was a really crappy explanation, sorry.
It would be perfectly OK to say something like "Wir sehen uns dann nicht bis zum neuen Jahr" if you're saying bye to a friend in November whom you know you won't meet till January.
It is a bit tricky with "Etage" and "Stock". Some count the first etage hence the floor you enter a building not as a "Stock" but call it "das Erdgeschoss", so the 1 in the lift is already one floor above ground. And for "Etage" it is more common to treat the ground floor as the first etage, so the difference is one floor, although that can differ depending on building and defintion. The actual thing is of course the same.