The gentleman who cranks the car grasps the crank with his thumb on one side of the handle and his four fingers on the other side (think of how people hold a screwdriver). People in the early 1900s would never crank a car this way; you put all of your fingers and thumb on the same side of the crank handle for safety. Everyone knew cranking those early cars could be quite dangerous, breaking fingers and wrists if the crank jumped back with a backfire.
Ford didn't start mass producing cars until 1908, meaning only the wealthiest of wealthy families could afford one in 1905. While it is technically possible to have a town where multiple cars are driving about, it is very highly unlikely. Only major cities like London or New York were likely to have multiple cars.
Wonderland is apparently set in the future, as a bowl full of modern Schlage (invented in 1920) and Kwikset (the famous "K" design key came out in 1958) keys meet Alice.
The title card is a full 11 minutes into the movie.