Hi Elizabeth,
Great to hear from you and great question. The rule is you must have a return plane ticket out of Costa Rica within 90 days of your arrival, even if you plan to stay six months. So as you say, you will have to leave Costa Rica and re-enter before your first 90 days is up. Keep in mind that when you re-enter you will need a ticket out of the country within 90 days of your new arrival date.
What many people do is buy a refundable ticket for their return ticket so they can change it depending on how much extra time they plan to stay. Not the cheapest option but it is what it is.
As far as a car, yes a someone on a tourist visa is allowed to buy a car. All you need is your driver’s license from home and your passport. At the end of six months you can sell your car. Cars hold their value so you’ll probably be able to sell it for what you paid for it.
Jason