B.Sc

Airport Authority of India regularly publishes requirement for their open vacancies regularly in newspaper and thier website. You are advice to look for open position and apply for position based on your education qualification. You are further advised to appear for CDS examination conducted by UPSC to join Indian Air Force.

The second option is much better. Civil services is the most sought after career choice. It will give you a great platform at a very young age.

CLAT is not a course. It is a common law admission test for 5-year BA LLB, BLS LLB or BBA LLB course from various National Law University such as Jodhpur, Hyderabad, West Bengal, Mumbai and so on. If you are interested is law, has good logical reasoning, good in communication and persuasion then you may go for law.
B.Sc has different specialisations, you need to zero on what you want to do.

Yes, there are many competitive exam after B.Sc such as SSC for staff selection in government jobs, UPSC,many state civil service exam, Bank PO, Bank Clerk exam.