Perhaps you should hold off, if you can, on buying a car -- whether you pay for it in cash or borrow money. Keep your liquid assets together to make your finances look better. Perhaps you should look into paying down as much of your debt as possible, keep your credit card balances low, and don't indulge in any high-ticket purchases.
Refinancing will entail pretty much the same process as when you bought your property and took out a loan. You had to qualify for the loan, and show you have the money for related expenses.
And since you have a home now, there are some guidelines as to how the banks set values for the property that is being refinanced. They will also send an appraiser to determine its current market value based, and what the bank's risks would be.