Looking at your criteria document (which is the same thing you sent me privately) this looks like a homework assignment. If so, then suggesting that you would pay me to do this for you, is very wrong.
Most of us will not do homework assignments. What we will do is critique your work and make suggestions for improvements. So far, RV and Daherb have given you good advice.
You asked; "Is there a way so when I select that the passenger wants to go 'one-way' from the drop list for example, it will only display the one way trip types in the next drop down list." This is a standard technique called cascading or synchronized combos. If you search here on those terms you will find instructions on how to do it. However, the question shows a lack of understanding of the airline industry. Flights have a start point and a destination. So essentially all flights are one-way. What is either one-way or roundtrip is the FARE not the flight. A passenger will book a trip as round trip because there is often a discount to do so rather then just book 2 one way trips. So you need to separate the issue of flights from fares.
You should laso have separate passenger and bookings tables. Your bookings table is essentially a join table, joining the passenger with the flight. You also need two tables for flight info. One table for the flights and another for the schedule. For example, you might have Flight 445 from NY to Chicago. It is scheduled for every Wednesday at 9AM. So you need a table that lists the departure dates separately from the flight.