If I Update New Plugin old functions will work?

This solely depends on which function you use. Removed function will not work anymore. You will have to analyse that in the exiting code.

you are mistaken here, i believe.  the "key features and functionality" list from the plug-in's description page is **NOT** an all-inclusive list of all functions the plug-in will contain, it is merely a passive description.  I can almost guarantee you that nearly all of the current functions will still be in the updated version (some may have been removed and some may have been replaced with iterated versions - the documentation on this is often very unclear unfortunately).

It is generic concept of code versioning. Whatever is present in latest version will work, if some features are removed from latest version it won't work.