Can a private pilot fly Light Sport w/o special training.?

Yes unless... the kifoxt is a tailwheel a version, requiring additional specific training and a logbook endorsement once completed

I believe the challenger has the options of floats, if you are wanting to operate one that did, you would need seaplane training and an endorsement. To do this, find an instructor who can give you seaplane instruction in an LSA qualified airplane....J3 Cub, Taylorcraft, Aeronca Champ/Chief, etc..this instructor can either be a "regular" CFI or a CFI-SP ....Also, remember...you can add Sport Pilot seaplane endorsement to your Private Pilot certificate as well, but you'll be limited to LSA qualified planes during seaplane operations...

You receive instruction from your CFI and when (s)he feels your competent you go for a "Proficiency Check" with another CFI who is seaplane qualified....this replaces the checkride with a DPE that is required to add an SES to your PPL

As I often say, what is legal is not always safe. If you have never flown either one of these models, it would be prudent to get transition training from a Flight Instructor that is familiar with the plane.

No not without medical training...but yes as Sport