The publisher should have made it clear that to use the Spine Runtimes you need a Spine license. If they didn't, then I would say that is misleading at best and dishonest at worst. Please see the Spine Runtimes license:
http://esotericsoftware.com/spine-runtimes-license
If the skeletons have meshes then yes, you will need Spine Professional. Your Spine license allows you to run any version of Spine. I suggest using the latest stable version, currently 4.1. You could also use 4.2 if you want to use physics, but 4.2 is currently beta. Note you need to keep the editor and runtimes on the same version:
http://esotericsoftware.com/spine-versioning#Synchronizing-versions
If they provided .spine
project files, you can open those with the same or newer version of the editor. You can then make changes and export new data files.
If they provided only data files, first run the version of Spine that was used to export the skeleton data. You can open the data with a text editor to see the version. Import the data into that version, then save the project as a .spine
file. Now you can open that with the same or newer version of the editor, make changes, and export new data files.
Lastly, I suggest setting up scripts to export all your projects. We provide some scripts here:
EsotericSoftware/spine-scriptstree/master/export
There is documentation there but we'll soon also publish a blog post and videos on how to use these scripts. The scripts make it easy to re-export all your skeletons so you can update to newer editor and runtime versions in the future.