My car hesitates at first when I put it in drive and step on the gas.

SOURCE: car hesitates and sputters

It seems like you have a vacuum leak in a hose some where. Check under the hood for any rubber hoses that are dry-rotted, cracks, or sharp bends in any of them.

SOURCE: I cannot get my car out of park

THERE IS A SYSTEM THAT WON'T ALLOW U TO SHIFT OUT OF PARK UNLESS YOU FOOT IS ON THE BRAKE.U CAN TURN THE IGNITION KEY ON AND SHIFT TO NEUTRAL THE START THE CAR AND DRIVE IT.IF U HAVE LEES THAT 36,000 MILES THE CAR IS STILL UNDER WARRANTY.IF NOT FIND A SHOP THAT IS FAMILIAR WITH THE SYSTEM

SOURCE: car will not drive in reverse, does not pick up speed when driving forward

TRY REPLACING THE TRANSMISSION FILTER LOCATED INSIDE THE TRANS. THE TRANS PAN MUST BE REMOVED TO ACCESS THE FILTER. A GALLON OF FLUID WILL NEED TO BE REPLACED AS WELL AFTER FILTER HAS BEEN DONE. THIS PROCEDURE WILL HELP THE OIL PUMP IN THE TRANS TO GET MORE FLUID AND HELP IT TO SHIFT GEARS. HOPE THIS HELPS. PLEASE KEEP ME POSTED. THANKS FOR USING FIX-YA AND FOR AN HONEST RATING TOO. BEST OF LUCK.

SOURCE: My mother's 2006 Dodge Caravan hesitates or

Tune up? Wires could be brittle and ignition power is being forced through the wasted wires

SOURCE: My intrepid dies while driving

It sounds (based on your description) like there is a Fuel problem:
1. Check the fuel pressure at the port on the Fuel Rail. Check especially when operating at higher RPM's than at idle or stop. At these levels there is enough gas being provided to keep the engine going. At higher RPM's the Pressure/Volume may not be enough causing the stalling.
2. When was the last time the Fuel Filter was changed? Change this and check operation before moving onto to #3.
3. The Fuel Pump. If the Fuel Pressure and Volume at the Fuel Port is falling at higher RPM's and the Fuel Filter did not help: It sounds like the Fuel Pump is failing. These will fail especially after they warm-up. This problem (losing power and dying) will happen more and more frequently and the Fuel Pump will eventually die all together.
You have to replace the Fuel Filter when you install a new Fuel Pump - it is part of the warranty.
4. The Fuel Injectors: If the Fuel Pressure/Volume at the Fuel Rail is fine, then it is not the Fuel Filter or the Fuel Pump. The problem is "downstream". It may be the electrical aspect of the Fuel Injectors or the mechanical side of the Fuel Injectors themselves. Check each Fuel Injector for correct voltage. If the voltage is correct - Pull and replace that corresponding Fuel Injector. I actually recommend: if you have to replace more that one Fuel Injector - go ahead and replace them all.