I believe there is a less limited suica card you can get (not a traveler), but I think you need a japanese address.
You don’t need a Japanese address. Simply visit any Suica vending machine, change the language to English, and purchase anonymous Suica.
There are various preloaded options you can purchase, but typically you cannot recharge e-money via cash.
I though there was a (blue?) one that japanese citizens could get, sent to their address.
No, there are no citizen specific IC cards unless you want extremely esoteric ones, like for senior citizens or children. All of the major nationwide mutual use transportation IC cards are freely available at the stations their operators carry. That's anything in the red box on this chart: https://en.wikipedia.org/wiki/Suica#/media/File:ICCard_Conne....