I have seen examples of ebikes with solar charging but only a few with a generator and never anything used for long trips. My question is...

Can you somehow safely hook up a generator to a running ebike?

My homemade design will include a trailer and if I could charge my bike with a small generator at the same time I am using it, the range is nearly infinite.

I have seen ideas on how the concept would work but premade bikes have safety features that prevent running while charging (for good reasons). I would like to build a new bike or bypass a brand name bike (preferably) in a manner that would not cause my battery to fry or cause any other electrical issues or hazards.

A generator can run 6-8 hours on a gallon of gas. That is 300-400 mpg if you run it the entire time. Add in some pedaling and turning it off for short durations, and 5 gallons could get you across the country.