In informix you have the "sysmaster" database and tables called "sys*" on your own database.
In the sysmaster , regular users have some limitations. If you don't have access for some table, use the "informix" user.
For information about status look the tables sysshmvals and sysshmhdr ,
to identify theirs structures read the file $INFORMIXDIR/etc/sysmaster.sql
answring your questions:
1) select * from sysmaster:sysshmhdr where name = 'mode'
to understand what is the mode value you can user this:
IBM - Status Codes Returned by the IDS Onstat Command
2) Is transparent, Informix work with backup online without stop users activity
3) already answered on my first post for you... but , CTRL-C / CTRL-V : select sh_narchivers from sysmaster:sysshmvals