You can do adaptor-signature based atomic swaps in Bitcoin without Schnorr; see https://eprint.iacr.org/2018/472 which has a full security proof (and security model, which is a nontrivial thing to define for transitive atomic swaps). Adaptor signatures can be used to make arbitrary sets of transactions atomic; and to even add transactions to these sets after the protocol has started. They are definitely not restricted to pairwise exchange, though in practice I expect you'll find it's hard to coordinate much else.

It is not possible to do a cross-chain atomic swap with only two transactions because you need at least one transaction on each chain, and the first transaction on each chain can be invalidated by publishing a conflicting transaction alongside it.