An Ubuntu persistent live USB is the same as a non-persistent live USB as far as using it as live media to install Ubuntu is concerned. The persistent storage space will not be carried over to the full installation, and any additional software installed by the user in the persistent live USB will not be installed on the newly installed operating system.
Additional software can be installed on a persistent live USB from the software app or from the terminal. Additional software that is installed on the Ubuntu live USB can be either reinstalled on the new operating system the same way as it usually done (the easy way) or a customized Ubuntu .iso image containing the additional software can be made by following the instructions in How to customize the Ubuntu live CD? (the hard way, not worth it unless you are going to install Ubuntu from the same customized live CD multiple times).
Files can be copied from the live USB to any other partition that mounted is mounted on the live USB. For example, if Windows is installed on the hard disk of the computer, the Windows NTFS partition can be mounted in Ubuntu and files can be copy/pasted between the mounted Windows partition and the Ubuntu live USB. If the partition is mounted in Ubuntu copy/paste can work in both directions.