How do I show running processes in Oracle DB?

I suspect you would just want to grab a few columns from V$SESSION and the SQL statement from V$SQL. Assuming you want to exclude the background processes that Oracle itself is running

SELECT sess.process, sess.status, sess.username, sess.schemaname, sql.sql_text
  FROM v$session sess,
       v$sql     sql
 WHERE sql.sql_id(+) = sess.sql_id
   AND sess.type     = 'USER'

The outer join is to handle those sessions that aren't currently active, assuming you want those. You could also get the sql_fulltext column from V$SQL which will have the full SQL statement rather than the first 1000 characters, but that is a CLOB and so likely a bit more complicated to deal with.

Realistically, you probably want to look at everything that is available in V$SESSION because it's likely that you can get a lot more information than SP_WHO provides.

After looking at sp_who, Oracle does not have that ability per se. Oracle has at least 8 processes running which run the db. Like RMON etc.

You can ask the DB which queries are running as that just a table query. Look at the V$ tables.

Quick Example:

SELECT sid,
       opname,
       sofar,
       totalwork,
       units,
       elapsed_seconds,
       time_remaining
FROM v$session_longops
WHERE sofar != totalwork;