Am I allowed to take the Retail Installment Sales Contract home with me before signing it, especially if I don't understand everything in it?

​Yes, you are allowed and, of course, you should never sign any contract you do not fully understand.  The Truth-in-Lending Act and its regulations require a creditor to make the required disclosures “clearly and conspicuously in writing, in a form that the consumer may keep”. 
 
Those disclosures include the Annual Percentage Rate, the amount financed (the amount of the credit being extended or money being loaned), the finance charge (how much interest you are paying back), the total of the payments, and the total amount paid (payments plus down payment).
 
Taking the contract home before you sign it is a great idea.  This allows you step back, away from the pressure of the salesman and his boss, and examine whether the deal is good for you, such as whether you can afford the payments.  Second, you can determine what other costs may be incurred like property taxes (not the same as sales tax) and higher insurance expenses.  You may decide the monthly expense is too high.  Third, you can shop the interest rate to see if you can get a better deal.  Fourth, if there are any terms you don’t understand, you can find someone to explain them to you. 
 
The Retail Installment Sales Contract is going to state there is no “cooling off” period so take your time. There really isn’t a rush to buy a car.