Sql-server – Will a clustered index improve performance of updates performed sequentially on that clustered index

A foreign key does not have an index by default. You have to create one.

In this case, I'd suggest either of these. It depends on relative selectivity of the 2 columns

CREATE INDEX IX_table2fk ON
              table1 (t2_col1, t1_col3)
              INCLUDE (any columns needed for the query)

OR

CREATE INDEX IX_table2fk ON
              table1 (t1_col3, t2_col1)
              INCLUDE (any columns needed for the query)

The INCLUDE will make the index covering to avoid key/bookmark lookups

You may have misunderstood the way a clustered index works - by definition the data is logically ordered in the sequence of the clustering key, although it's possible for the clustered index to become physically fragmented as page-splits occur when new data is inserted.

If you want to reduce fragmentation either REBUILD or REORGANIZE can be appropriate. The rule of thumb is to do nothing when fragmentation is below 5%, REORGANIZE when fragmentation is between 5% and 30%, and REBUILD when fragmentation is above 30%.

Index fragmentation is recorded in the DMV sys.dm_db_index_physical_stats. See also the MSDN page on REBUILD/REORGANIZE

It's worth noting that unless you are running SQL Server Enterprise edition, REBUILD cannot be performed on-line - meaning that your table will be inaccessible for the duration of the command. REORGANIZE is always carried out on-line.