as a first step to answering (2), I just applied the patch below, and it
seems to build the reference in texinfo format.
diff --git a/src/sage_setup/docbuild/__init__.py
b/src/sage_setup/docbuild/__init__.py
index 0bd52a6..9ddf7d4 100644
--- a/src/sage_setup/docbuild/__init__.py
+++ b/src/sage_setup/docbuild/__init__.py
@@ -238,6 +238,7 @@ class DocBuilder(object):
linkcheck = builder_helper('linkcheck')
# import the customized builder for object.inv files
inventory = builder_helper('inventory')
+ texinfo = builder_helper('texinfo')
##########################################
# Parallel Building Ref Manual #
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