Is there any way to list down parameters' data type in each of the function.
Yes, use the pg_get_function_identity_arguments()
function:
The following will create a SQL script to alter all functions from the someschema
schema:
select 'alter function '||nsp.nspname||'.'||p.proname||'('||pg_get_function_identity_arguments(p.oid)||') owner to newowner;'
from pg_proc p
join pg_namespace nsp ON p.pronamespace = nsp.oid
where nsp.nspname = 'someschema';
You can spool the output of that into a file and then run that generated script.
If you have function names that would require quoting, you probably need to use quote_ident
to concatenate the function names.
You can wrap all that into a function and use dynamic SQL to make life easier if you need this on a regular basis.