I want to overwrite the current K2 files with the latest version of K2. There seems to be some issues with some of the files.

Does that delete K2 items or configuration? does this require a ftp connection or can I do it through the joomla site?

You should backup your site first....
Then use the joomla component installer and install k2 over the top of your current install.
Your items and categories should be intact
You will loose any changes to the core files you have made, and if you are using overrides they may need to be adjusted.
Again, be sure to back up first!