1: In ASE 15.7 ESD#2 or later, yes (use update statistics..."with print_progress = 1"). In earlier ASE versions, no.
2: No: Optdiag operates per table. Statistics apply to a table's columns, not to indexes. Whether or not those columns are indexed is another matter. You can have statistics for non-indexed columns (though that would perhaps be a bit unusual).
The relation between statistics and indexes lies in the ASE query optimizer: it use column statistics to determine which index would provide the most efficient access for specific parts of a query.
3: in 15.7 ESD#2, use the 'hashing' option for update statistics. In earlier ASE versions, you can try the 'sampling' option (YMMV).
HTH,
Rob V.