Will I be able to open sldprt files from 2014 in Solidworks 2018 or 2019?

Yes and I believe this is applicable for other cad tools as well.

You bet!

Imagine if you could not. Every year you'd install a new version to get all the latest and greatest tools, but you'd need to keep all the previous versions around forever. Or you would have to convert all of your files every year.

Joseph Cottingham wrote:

 

Is there full forward compatibility with Solidworks CAD?

Yes, you can, but if you save them with SW2018 or SW219 you will no longer be able to open them with SW2014.