Yes, there used to be several manufacturers who offered gas powered semi trucks. GMC offered the 366 Cubic Inch V8 for many years in heavy trucks and they used a 550 CU In V8 in some trucks including Fire Trucks and big construction trucks. Gasoline engines are not very efficient for heavy continuous loads that heavy trucks demand so they just don't have the durability that diesel offers. Diesel fuel has more BTUs per gallon and can provide more work for the fuel consumed. The old gasoline powered trucks often got in the two to four mile per gallon range while todays biggest diesel trucks achieve fuel economy in the 7 to 8 MPG range. Fleet trucks generally use smaller diesels int their trucks, around 375 to 425 HP, so they get a little better mileage. Independent truckers struggle to get the shortest turn around time possible so the run up to 600 HP in their trucks but pay for it in lower MPG, around 5.5 to 6 MPG. Today manufacturers still offer gasoline engines in trucks up to 26,000 GVW but I am not aware of any trucks bigger than that with gas engines. Old truckers will tell stories about climbing highway grades at 10 to 15 MPH with their gas engines ready to overheat but modern truckers now go over the same grades at 45 to 55 MPH in air conditioned comfort using half the fuel.

I remember seeing and hearing a full-sized tractor-trailer delivery truck carrying mattresses back in the late 70s... another trucker standing near me commented on the "gas buggy." Listening, it became obvious that the thing had an automatic transmission too... So the answer to your first question is yes. I can't comment on the second question.

Yes, although in those days, loads were lighter and trucks were smaller than they are now. There were any number of pejorative names for such trucks. One of the largest trucking companies in the U.S., Werner Enterprises, was started by Clarence Werner with one Ford gas truck. From there he developed a company of some 8,000 trucks.