Is it acceptable to give out information about an unpublished paper in an application?
Whoever told you not to circulate the paper is the person to ask. If you were specifically asked not to do so, the author could consider it a breach of trust to  mention the ideas/results without clarifying the extent to which you can make claims about the project. Maybe they do not mind a general overview, only the paper, but this is something you need to find out from them.

"I will definitely be including it in my applications" is a problematic sentence under these auspices. It is not a good idea to mention the journal, either. Say, it's a top-tier journal. Anyone can submit a paper, but at this stage it is not accepted yet. 

In addition, you probably should get more detailed advice from a trusted mentor on how to develop your application.