> >>with allowed values of "all, mod, ddl, none" with default "none".

OK, here is a patch that implements #1.  Here is sample output:

        test=> set client_min_messages = 'log';
        SET
        test=> set log_statement = 'mod';
        SET
        test=> select 1;
         ?column?
        ----------
                1
        (1 row)

        test=> update test set x=1;
        LOG:  statement: update test set x=1;
        ERROR:  relation "test" does not exist
        test=> update test set x=1;
        LOG:  statement: update test set x=1;
        ERROR:  relation "test" does not exist
        test=> copy test from '/tmp/x';
        LOG:  statement: copy test from '/tmp/x';
        ERROR:  relation "test" does not exist
        test=> copy test to  '/tmp/x';
        ERROR:  relation "test" does not exist
        test=> prepare xx as select 1;
        PREPARE
        test=> prepare xx as update x set y=1;
        LOG:  statement: prepare xx as update x set y=1;
        ERROR:  relation "x" does not exist
        test=> explain analyze select 1;;
                                             QUERY PLAN
        ------------------------------------------------------------------------------------
         Result  (cost=0.00..0.01 rows=1 width=0) (actual time=0.006..0.007 rows=1 loops=1)
         Total runtime: 0.046 ms
        (2 rows)

        test=> explain analyze update test set x=1;
        LOG:  statement: explain analyze update test set x=1;
        ERROR:  relation "test" does not exist
        test=> explain update test set x=1;
        ERROR:  relation "test" does not exist

It checks PREPARE and EXECUTE ANALYZE too.  The log_statement values are
'none', 'mod', 'ddl', and 'all'.  For 'all', it prints before the query
is parsed, and for ddl/mod, it does it right after parsing using the
node tag (or command tag for CREATE/ALTER/DROP), so any non-parse errors
will print after the log line.