Can you use synthetic oil in a 25HP Kawasaki engine?

I am not an expert in oils, but I have heavily researched lubricants lately. From my research, I have not found a single application (although there may be some out there) where you could not use synthetic oil. I have also not found any application where synthetic oil would not offer superior longevity or cold temp characteristics.

There are however many differences in oils and many different manufacturer specs that should be followed. I would always check the manufacturers reccomendations to meet any specific requirements that they reccomend and then ensure that the oil meets those minimum requirements. Look at the owners manual. If it says to use an API engine oil, then you could use any engine oil that meets the viscosity requirements listed in the owners manual (they will likely just be based on temps) that has an API rating, which will be just about any engine oil for gasoline engines.

That is my 2 cents. Checking that owners manual and comaring specs is essential IMO.

Yes, and I highly recommend you do in any air cooled engine.