To build a private network for Cardano, you need a Cardano SL; a collection of binaries that constitute the backend and the election based wallet called “Daedalus”
That’s incorrect. You’d need to implement some process or protocol using that token and/or the blockchain itself (e.g. transaction metadata) before you could say you had a Level 2 on Cardano.
No, because let’s say we wanted to build a system entirely on transaction metadata… i.e. the unit of information or value is included in a native ada transaction. You could build a Cardano Level 2 system that way without creating any tokens.
With the upcoming hardfork it’ll be possible to include even more information inline with transactions so these types of systems will become even more feasible.
No, I don’t have any current examples of this idea but some colleagues & I last year discussed building a publishing Level 2 system on Cardano where most of the P2P market data would be encoded in the transactions themselves. Some types of native tokens would probably have been desirable for this, but not required.