Forcing Notions with Unknown Real/Cardinal Preserving Situations Question. Is there any set forcing notion $\mathbb{P}$ in one of the following categories?
(a) $\mathbb{P}$ preserves cardinals but it is still open whether $\mathbb{P}$ adds reals or not.
(b) $\mathbb{P}$ adds no real but it is still open whether $\mathbb{P}$ preserves cardinals or not. 
 A: There are certainly plenty of examples for question (a).  The notions of forcing $\mathbb{P}$ arise in the context of iterating proper notions of forcing where each iterand is known not to add reals, but we don't understand what happens in the limit.
Some specific examples:
(1)  Forcing related to the Moore-Mrowka problem and CH
The notion of forcing isolated in this paper is proper and adds no new reals while accomplishing some topological task. If we let $\mathbb{P}$ be the limit of a countable support iteration of length $\omega_2$ where each iterand is as in the paper, we know $\mathbb{P}$ preserves cardinals (assuming GCH) but it is open if it adds new reals.
The relevant paper is:
Todd Eisworth, Totally proper forcing and the Moore-Mrowka problem, Fund. Math. 177 (2003), no. 2, 121-136.
[The consistency result we were looking for has been obtained in another way, but we still don't understand what happens with this particular notion of forcing.]
(2)  Justin Moore's "measuring with CH" problem
The situation here is as in (1), where we have a proper notion of forcing that accomplishes something without adding reals, but we do not know what happens when things are iterated.  See section 7.2 of
Todd Eisworth, Justin Tatch Moore, and David Milovich, Iterated forcing and the Continuum Hypothesis,  Appalachian Set Theory: 2006-2012, James Cummings and Ernest Schimmerling   eds., Chapter 7  207-244,  Cambridge University Press (London Mathematical Society Lecture Note Series v. 406)  2013.  ISBN:9781107608504
