Catkin - 26d and 31a share a common four letter word - not two letters as you suggest.
26d is an icy area (think of what the perma-frost area with dwarf vegetation is called) surrounded by a two letter word demanding peace (and quiet) - all going west (reversed). This will give you your tough men!
31a starts with a longer word which has a short-form of A, followed by a fish (think of a fast swimming ocean fish) and a short-form for caught both reversed (on the rise). That will give you something chewed in S Asia.
Parsing 20d had me puzzled for a while - but it's very clever! Think of the collective noun for crows and preposterous has "reversed" as one of its meanings.
Hope this all helps!