I bought some RE units today in 3 transactions (5 units each time). Should I have to place as many orders on the RTA website or just one consolidated order for RE units is enough?

Irrespective of the number of orders you have placed while purchasing Rights Entitlements (REs), you can send one single application for Rights Issue combining the total units of REs you have in your demat account.

For Example - if you have placed 3 buy orders each for 5 units of REs, you can send a consolidated application for 15 rights shares on the RTA website.

To know more about Rights Issue, get the SEBI FAQs here, NSE FAQs here and BSE FAQs here.