Welcome to the site.
I will answer #5 first, like evey one else. No, it never gets old. I get excited every time I get in one of them. I can't help but smile. You will also waste hours standing on the sidewalk looking back at it on the way to your front door, or looking out of the window at it. Yes, it is true.
There is a very good How-To Document section that you can find tons of info on how to do things. We are in the process of upgrading this in the next couple of weeks.
As far as the cooler, if you look under the car, you will see where the transmission hoses go into and out of the radiator. If it goes from there to some other cooler, you will know that you have one. There may be an inline transmission filter too.
Visit often and we are here to help you as we can. Good luck on the project and read the manual so you will discover all of the fun features on this special car.