1.What affects the table index tree, is it updates/inserts/deletes ?
Updates: Each update on the indexed column is treated as a delete followed by an insert in the index.

Inserts/Deletes: They can affect performance in a B-tree index if they exceed 10% and the inserted values do not follow normal distribution.

2.I have a index defined over three columns in a table, and the table gets updated very frequently but those columns indexed are not updated.
Would those updates also affect the index tree..Do i need to rebuild the indexes in sucn cases too..?
No. If the updates don't cause lot of records to be migrated.

3.When does rebuilding index tree take more time, is it when the table has more number of records or the table had involved in more number of transactions ?
When the table has more records. But if you are rebuilding the table 'online' and the table is having high transactional activity, you can expect it to take more time rebuilding.