Sql-server – Rebuilding Index – sort in temp db

This option only controls where intermediate sort space (not the index itself) is allocated from. See here for a more in-depth description of how tempdb is used when indexes are created.

You still need enough free space in the data file(s) to accomodate a second copy of the index, because SQL Server must lay down the new index before dropping the old one (it doesn't overwrite in-place).

The amount of space needed in the log file depends on the recovery model of the database. Check out this blog post for a comparison between FULL and BULK_LOGGED recovery models (SIMPLE would be the same as BULK_LOGGED -- in other words, minimally logged).

Index rebuild operation is DDL and thus may lock the underlying table preventing you from updating it. However queries by nature do not lock (unless FOR UPDATE clause is specified) and can read from objects even if they're locked, thus, generally, no problems will arise during the index rebuild while queries are running (maybe except for some performance degradation during rebuild).

If you want to be able to update the table having the index which is being rebuilt, you can specify ONLINE clause:

SQL> alter index table1_pk_idx rebuild online;

Otherwise the session performing DML will wait until the index is rebuilt.

For more info on index rebuild, ONLINE clause, and index rebuild restrictions, read the section "Rebuilding an Existing Index" in Administrator's Guide, and the section "ALTER INDEX" in SQL Language Reference.