Error java.sql.SQLException: ORA-01555

Gaius is right, use DBA_TABLES for NUM_ROWS and DBA_SEGMENTS for size:

select owner,table_name,num_rows,last_analyzed from dba_tables;

The num_rows count is as of LAST_ANALYZED date, which should be close enough even without running DBMS_STATS.

For sizing:

select owner,segment_type,sum(bytes)/1024/1024 size_mb
from dba_segments
group by owner,segment_type;

or (depending what level of details you need):

select owner,segment_name,sum(bytes)/1024/1024 size_mb
from dba_segments
group by owner,segment_name;

For LOBs you'll need to join it to DBA_LOBS, for indexes to DBA_INDEXES, for tables to DBA_TABLES. A lot will depend on your specific requirement. Since you mentioned you are trying to figure out used space in tablespace it might be as simple as:

select sum(bytes)/1024/1024 size_mb
from dba_segments
where tablespace_name='YOUR_TBLSP_NAME';

Your solution would really work only with small DB as it would not be feasible to read all data on large DB.

I am hesitant to post how to address ORA-1555 as in this case this it NOT your primary issue but just for completeness - you are on 10g using automatic undo management so your DBA would have to increase undo_retention in your database (the ixora link is relevant to a DB without auto undo management).

Per the Oracle Docs and MetaLink support note 66431.1, the standard undo mechanism is not used by LOB segments, which have their own page versioning (controlled via PCTVERSION and the LOB_retention_clause).

"Snapshot too old" generally means that a transactionally-consistent version of your data could not be hold long enough because of lack of space. It might be that your PCTVERSION setting is too strict and effectively causes any new update to invalidate the consistent version(s).