Continuity doesn't mean the wire can carry a load. If there is 1 strand of wire still good, it will pass the continuity check but when you apply power 1 strand is not enough to carry the electrical load.
Mine did not need to be coded. I installed this on my 2003 and I had to add two wires to the green plug and tap those into the "I bus". The closest I bus wires are at the LCM. Just make sure those two wires are there.
I'm always afraid that I'm going to break something yanking the door off. So, I found a universal torx extended bit that can get to the two screws with the door held partially open.
Get an aftermarket key with transponder and an AK90 programmer (to program the transponder to the EWS). You will have to have someone cut the key blank but still way cheaper than a factory key. I've got two aftermarket keys, and they've worked great for the last 5 years.
Nope, it's sewn into the top. Most of our tops look like that age. It shouldn't leak from what I understand that was sewn into the top to stiffen the edge and to help the top fold correctly.