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.
Interestingly, the idea of your referenced source, multi-hop locks, shares the concept of employing homomorphic hash functions with this proposal.
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.
I doubt it. Using this proposal:
Alice issues tx1 on aliceChain sending m aliceCoins to Bob hash-locked with H(s1) after privately handing Bob (t, H(s1), H(s2))
Bob does the same by issuing tx2 on bobCahin hash-locked with H(s2), AFTER tx1 is confirmed on aliceChain.
Now Alice should wait for tx2 to get confirmed before spending its outpoint and Bob should wait for Alice spending tx2 (and revealing s2) to be able to calculate s1 = t-s2 and spend tx1's outpoint.