To connect to an idle instance means that you are connected to an Instance/database/Server that is SHUTDOWN. So you need to STARTUP so the database is accessible.

A segment is any object that requires physical storage outside the data dictionary. So if you create a table, it is also considered a segment. Same is true for indexes.

DBWR will not write to a datafile when the tablespace is offline.

Maxextents on a TABLESPACE is the max # of extents (chunks of space) that any 1 segment is allowed to have in that particular tablespace. Your tablespace space is limited to the size of your datafiles.