Will I be able to open and view LabVIEW 2016 VIs in LabVIEW 2013 at all? I just need to be able to review the VI's implementation as much as possible with 2013 version.
If you have a copy of 2016 you can do a "Save for previous version" that allows older versions to open it, but the 2013 version can't open them by default.
LabVIEW has backwards compatibility (mostly, besides deprecation) but not forwards.
Besides the obvious option, you could ask the developer to save the project / VIs for a previous version. Or, crudely, get screenshots of the block diagrams.
Although it seems likely (given you have source code in 2016) that someone you work with has 2016 installed, if that's not true (or you really don't like talking to them) there's also a Version Conversion subforum where you could ask for someone else to convert the VIs.
