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You are probably not seeing the anchor bolt and block near the base of the battery. Remove this bolt and remove the cables, battery will come right out.
Get estimate at a body shop. The door may be repaired and adjusted and the dent pulled out at a much lower cost than a replacement. It could just be a crease dent at the hinge which they can repair.
Can you describe the noise? Possible stabilizer link, CV joint, ball joint issue etc. Is there any vibration or pulling of the steering wheel while driving? More info. please or take to a shop for a diagnosis.
No it is not. The bearing in the fan assembly has probably failed and needs replaced.
There is quite a few possibilities. The only way to find out is have a front inspection by a good shop and have them test drive.
The blend door actuator may be faulty and isn't switching over to the heat side of the HVAC system. Need to get a look at it and throw the switch to see if it is functioning.
First, take it in for inspection. Could be as simple as being low on transmission fluid. Get inspection done at a reputable trans. shop first. May just need a little TLC.
Need to have charging system inspected. Possible alternator or battery issue. Suspect the alternator.
Usually this is a water pump issue on the PT cruiser and replacing it is a large job. You may want to take this one to a shop to do. If not, here is the process : http://www.ehow.com/how_7535906_change-water-pump-pt-cruiser.html
Agree #1. Get the read and have them print the ticket and give it to you. Then you can post everything on it to this site.