You might be able to do both tasks with a combination of the free Adobe Reader and any print-to-PDF virtual printer. Adobe Acrobat Reader has features both for printing booklets (2 PDF pages per output page) and posters (splitting one PDF page into 2 output pages). Try to use these 2 features with a virtual printer that saves PDF to convert your PDF from and to booklet format.
One such virtual printer is LEADTOOLS ePrint printer driver (Disclaimer: I work for the vendors of ePrint). The driver installs like any regular Windows printer and accepts print jobs from Windows applications including Adobe Acrobat Reader. It can then save the print job to PDF again. One feature that could be useful in ePrint is Layout option in the Enhanced Printing Options Dialog. This Layout option allows you to specify values like Single, Booklet, Double, up to 16X. Using this option in conjunction with Adobe Acrobat Reader’s printing options (like Booklet and Poster) to achieve different combinations of pages per output page.
If you decide to try that, I recommend doing that with the free evaluation of ePrint before you decide to purchase, to make sure you’re getting the results you expect. Also, if you try that and don’t get the results you want, you can contact the support email address for free (ePrintSupport@leadtools.com), or you can simply un-install the evaluation to remove ePrint.