The jack could not have pierced the fender, it isn't that tall.
When Mrs. Grundy turns on the car radio while the girls are asleep she is clearly miming the action. Her whole hand is visible.
When they pull to the restaurant to use the phone, they rush inside to use the phone, even though an outside phone booth is clearly visible to the right of the building.
If they were truly spending the night in the Everglades then they are off course to Miami.
Lucy, Ethel, and Mrs. Grundy pull over to a roadside diner so that they can make a phone call to the police. Once inside the diner the counter man tells them that phone is out order and thus there is no way to make a call. However, notice in the view outside of the diner that there clearly is a telephone booth from which they could of made a phone call from.
Assuming that banks were closed when Lucy realized she lost the train tickets, she and Ethel would of had many different avenues in which to get new train tickets or find a way to Florida before having to share a ride with Mrs. Grundy. Despite not having enough money on hand to buy new tickets they could of bought new tickets on credit (many times in the series Lucy says she has a credit card), they could of inquired with the railroad company on how to replace lost tickets, and if necessary asked friends or family, or had them wired, the necessary cash to buy new tickets. In addition they could of also seen if the money the had on hand was enough for bus fare to Florida.