The answer to your questions: yes and yes. I am assuming this is your first ascent of Whitney and it would be in your best interest to get as much time at elevation as you can the days leading up to the Whitney hike. Horseshoe Meadows (elevation 9,900 ft.) is very close by to the portal and is an excellent place to acclimate. If you have time, you can day hike up to some high elevation passes from either the cottonwood pass trail head or the New Army pass trail head (cottonwood pass or new army pass (11,500 ft to 12,300 ft +/-).
Sleeping in a car or a truck is a personal choice. I like to sleep in my vehicle. It's big enough for me to stretch out and get a great night rest. But if you don't have a vehicle that can accommodate you or multiple people then staying in a hotel might be best.
Hope this helps!