It is possible to claim for more than one car. The IRS form has two columns. However, you'd have to owe a lot to make it worth your effort based on the way the credits are applied. No carryover of excess credits is allowed. How it applies to you is not simple and you'd best compute the numbers on your personal situation, or talk to your accountant.
It must be put in service during your tax year, which basically means for most people by December 31st.
I see no requirements on how long you must own the car. Technically the program doesn't apply for cars purchased for resale, but there's no details as the IRS is still working out the details of the rules. See IRS form 8936 for more details.