Having different Table space for different indexes of same table, will causes any performance impact

1. You should be fine; the rowid would be a show-stopper if you were using it
2. Temporarily, there would be "holes" in the data files, but Oracle will fill them in without any intervention. Ensure you have automatic tablespace management enabled.
3. You can invoke that command but no need to; let Oracle take care of it
4. The person that stated that probably meant there was a one-time hit, or he didn't know what he was talking about, or using an old version. You tested; his environment may have had a rat's nest of views.

The whole point of an INDEX REBUILD is to make the processing of data more efficient. This means that when possible it reorganizes the data to reduce the number of pages (according to the fill factor and other limitations) used for that index (whether it is a PK, unique, or non-unique index)and to order the rows of data more efficiently within the used pages and extents.

Therefore, it will reuse existing pages as the first choice. This should result in less storage being used. Of course if the indexes are modified, this could expand the amount of storage needed, depending on the modification.

Using tempdb to rebuild indexes can be a performance boost, but is unlikely to dramatically affect the required storage.

In this case you should definitely rebuild the indexes.

Note that this will not reduce the physical size of the .mdf and .ndf files. It will free up space that can be used as tables in the database expand in size.