Issues when splitting one long paper into two papers
Yes, it can be problematic if content is repeated verbatim in different sources, as it can be viewed as "self-plagiarism." The excellent Retraction Watch blog has an article that outlines the Committee on Publication Ethics's (COPE) views on the subject of when self-plagiarism merits retraction. In their proposal, the kind of reuse you're talking about could easily be considered plagiarism, even if it were cited as a quotation of the other paper.

The reuse of plots is also problematic—you'd need to make sure that reuse is allowed by the publisher of the article which appears (or which is accepted) first. If not, you can get yourself into trouble in that way as well. (Ultimately, this is how the fraud in the Jan-Hendrik Schön scandal was finally exposed.