We'll need to be aware of free space during this process. If the data on the old partition is larger, you'll need to selective in what you bring over. It's not unusual to find lots of old files that are no longer needed that can be discarded. However, if all the data needs to be transferred, you would need an external drive to backup in order to make the complete transfer.
Most apps can be brought over by drag and drop. Some apps like Adobe and Microsoft need to be installed using an installer to get all the bit and pieces required. During this process make sure your apps are updated. Chrome and Firefox especially are updated frequently and need to be the latest version.
See this article for details. Move your data to a new User or a new Mavericks partition
http://www.needhelp4mac.com/2014/06/move-your-data-to-a-new-user-or-a-new-maveri cks-partition/
While it was written for Mavericks the same steps apply. Details in the top section (Transferring files from one account to another on the same Mac) contain the details on what you want to bring over). The bottom section (Transferring files when data is another drive or partition) explains how to setup for the move.
Note: I like to be on the cautious side when moving over data. You can always go back and bring over additional data if needed.
We can help with specific questions as they come up.
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