Clausal arity can't be expressed structurally at the surface level. I'll modify the Catalan example (I'll use llegir "to read") and add two more phrases:
(1) faig llegir - complex predicate (CP), monoclausal
(2) vaig llegir - not CP, monoclausal
(3) vull llegir - not CP, biclausal
The corresponding syntax trees are identical (up to node/edge labels).
Complex predicates present a problem to unification grammars. Alsina proposed a solution (in his paper on causatives in Romance and Bantu 1997, page 236) but it's only a technical workaround that "breaks" the monotonicity of unification. We could add semantic forms (SF) to tree nodes in any dependency grammar (faig in (1) would have cause(subj,*) and the main verb would have, in this case, llegir(x,y)) but they can't be unified so it's a useless formalization.
As to the second question, I think that most complex predicates are "chains" as defined by O'Grady but there are counterexamples (CPs with "vertical" gaps/discontinuities). But CPs aren't idioms so it shouldn't be particularly surprising. (There are quite a few papers by Butt on Urdu, which is heavy on CPs, with LFG analyses - BTW LFG has "chains" since its inception in 1982, they're just called differently.)
Note that "chain" isn't a precise term because it suggests something one-dimensional whereas the definition allows general connected subgraphs (and there are examples of "chains" that are nontrivial (sub)trees, i.e., not simple paths).
Note that chains DON'T work at the level of surface syntax. O'Grady defines them explicitly at the lexical level and gives examples why they can't by applied at the syntactic level (as they'd be discontinuous). At the lexical level (Alsina's argument structure) they make perfect sense.