RIE CEE

You can pay through Canara Bank/ HDFC e-challan) mode offline.

Please check for your eligibility to appear for the RIE CEE exam from the criteria mentioned at the link provided below:
https://www.shiksha.com/teaching-education/exams/rie-cee.

Please check for the RIE CEE exam pattern at the link provided below:
https://www.shiksha.com/teaching-education/exams/rie-cee/pattern.

Yes, RIE CEE is a competitive exam. A brief summary of the RIE CEE is mentioned below:
The National Council of Educational Research and Training (NCERT) conducts Common Entrance Examination (CEE) in order to provide admission to candidates in teaching courses offered at Regional Institutes of Education (Rides). Rides are located at different locations in the country including Ajmer, Bhubaneswar, Bhopal, Mysore, and Shillong. To read more about the RIE CEE refer to the link provided below:
https://www.shiksha.com/teaching-education/exams/rie-cee.

Please refer to the link mentioned to get the details about RIE CEE exam. Link: https://www.shiksha.com/teaching-education/exams/rie-cee.

Yes, as it sounds Bachelor of Science. It means that it is a Bachelor's degree course and you can take IAS exam after this.

Please refer to the link provided below where details regarding payment for application fee is mentioned (Both Offline and Online method).
Regards.
https://www.shiksha.com/teaching-education/exams/rie-cee/application-form

Yes, nowadays, certification courses of everything are available so you may learn an Indian language at certification level. This will help in many ways. Secondly, you need to consult with the particular college from which you want to do.