I know a little bit about your question #1. I currently live in southern OH so don't typically need one, but much of my family live in CT, NJ, NY, and PA. When I looked into it for the few times a year I'd need it, I found that you only need an EZ-Pass (or equivalent) from one state. You could travel from Chicago, IL to NYC, Boston, Philly, NJ, etc. and the toll roads along the way would all accept your transponder. So you don't need
one for each state, although you can
purchase one. I believe the KS and FL systems are also compatible; I don't know about CO or TX.
As to #2 question (discounts), my understanding is that those vary with the agency that owns/administers the road/tunnel/bridge, but that most if not all apply to any transponder. The discount is essentially for not causing delays and for reducing the toll-taking expense by not requiring a manned lane. The page at https://www.ezpassnj.com/en/about/plans.shtml
has some details regarding NJ.
#3, again from the NJ website, indicates that they can detect you're towing and charging accordingly. See https://www.ezpassnj.com/en/faq/misc.shtml
, question "I sometimes pull a camper or trailer with my vehicle. Can I still use my tag?" I'm not sure if this is the same in all states or not, but you can searching the web to learn more.
#4, again from the website, states that you establish a prepaid EZ-Pass account using cash, credit card, or personal check.