Ok, I can actually answer all of your questions rather easily.
1. The model of your Trio is determined easily by the word "Trio" located on the battery near the atomizer coupling. If "Trio" is RED, then it's a redline. If it's not, it's a Trio gold/standard.
2. The redline and standard atomizers ARE different. Although you may get a standard atomizer to work now and then in your Redline, you could actually damage the atomizer and battery as well. There are specific atomizers sold for each model, and online they state "only for use with Trio _____".
3. The model number for the Redline atomizers is: N1008121, and it is stamped onto the side of the atomizer.
4. They CAN use the e-liquids, but generally do actually work better using the Fifty-One brand cartridges.
5. EVERYTHING from Fifty-One and it's sister affiliate sites (i.e. Smokefreeonline.com) are RIDICULOUSLY overpriced. I have no qualms with my Trio, but I wish I had someone donate it to me like u were so lucky to have. There are MUCH better systems out there that are easier to use, customize, maintain, and find supplies for, that even if the Trio WAS the best e-cig on the market (it's not), it still wouldn't be worth the purchase.
6. My recommendation is the Joyetech 510 (a.k.a. Titan, Joye 510, etc). It can be customized until your face turns blue, there are no shortage of sites that sell supplies compatible with it, and there is a starter kit to pretty much fit any budget. Essentially, it's the Harley-Davidson© of e-cigs. It may not be THE best on the market, but it certainly is just about the most popular, most replicated, and most customizable. It gives off excellent vapor, great throat hit, decent battery life, and the price is excellent.