Yes, they do. Since you're unsure about the chip in your car, I would remove it just for a peace of mind. I would hope it's a custom burned chip created during a dyno session. I don't have experience with them as I've always had my cars on the rollers so, I wouldn't know much about them.
The...
I wouldn't remove it. The spoiler-less deck lid looks very odd to me. I would understand if you were removing the GT spoiler, but no way would I remove something that makes the 03/04 Cobra so distinct from all other Mustangs of that era...
IIRC, the spoiler is held on by 5 bolts and a double...
Did the PO tell you who tuned it? They might have the stock tune on file if it was tuned with a handheld
Anyhow, I would think you shouldn't have any problems taking the car to your local Ford dealer and have them reflash your ECU back to stock.
It depends on what type of batter tender you use. Some will overcharge your battery. I use an automatic battery tender that goes into float mode once it has been fully charged. I keep it on the entire duration as it gets pretty cold around here (below -50 at times).
I thoroughly wash my car, fill up on gas, add fuel stabilizer, throw on the trickle charger, car cover, and leave it from the beginning of Oct - late April. If you don't have a heated garage then I would suggest putting carpets/cardboard boxes under each tire. Never had any issues and I don't...