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Question One
An excise tax is a tax that is added to products that are produced domestically.  For example, if a local government levies a tax of $.07 on a pack of cigarettes, then $.07 is added to the cost of each pack of cigarettes (Baye and Prince, 2017).  The excise tax will increase the price of a product and therefore the demand decreases.  This is a negative and linear response to the tax.  This depends to a degree on the elasticity of the price.  Elasticity is how much the price change effect the demand.  Not all products are affected equally.  The change of price will affect some products more than others.  For some products, an alternative can be used.  For others, like cigarettes, the excise tax may increase the demand for illegal products (Scilly, 2016).
The federal excise tax on gasoline is used for the highway infrastructure.  Gasoline also has a state excise tax.  This varies in each state.  It also goes toward the upkeep of roads (Cautero, 019).  The demand of gasoline is affected by the price of gas.   When the price of gasoline increases, consumers respond by purchasing vehicles with better gas millage and the may limit the trips they take (Thompson, 2017).   
Baye, M. R., & Prince, J. T. (2017). Managerial economics and business strategy. New York, NY: McGraw-Hill Education.
Cautero, R. (2019, February 07). What Is the Federal Gasoline Excise Tax Rate? Retrieved June 17, 2020, from https://www.thebalance.com/what-is-the-federal-gasoline-excise-tax-rate-4585178
Scilly, M. (2016, October 26). How Does an Excise Tax Change the Quantity Demanded? Retrieved June 16, 2020, from https://smallbusiness.chron.com/excise-tax-change-quantity-demanded-18399.html (Links to an external site.)
Thompson, C. (2017, March 08). Rising gas prices are a growing threat to the American way of life. Retrieved June 17, 2020, from https://www.businessinsider.com/how-rising-gas-prices-impact-economy-2017-3

Question 2
Price elasticity of demand measures the responsiveness of quantity demand to a change in price( Baye and Prince p.66). This concept becomes helpful for managers to see when they need to raise prices or lower them due to how they are responding to the every day market. An excise tax is a tax on each unit of output sold, where the tax revenue is collected from the supplier(Baye and Prince, p.41). An example of this would be when the government levies a tax on gas for $.50, meaning suppliers will have to pay that $.50 a gallon each time a gallon is sold, this can affect prices. The excise tax shifts the supply curve to reflect the change in price after the new tax amount. Excise tax has a relationship with price elasticity because, one affects the overall price of a product in a market, and the other is how well it responds to this change. Price elasticity when it comes to excise taxes on gasoline would help make sure they suppliers wouldn’t lose any money on selling gas just because of a  tax that was inputed on it. 
Reference:
Baye, M. R., & Prince, J. T. (2017). Managerial economics and business strategy. New York, NY: McGraw-Hill Education.