Microsoft Certifications

It all depends on your job role and career aspirations. If you are working on Microsoft technology, then obviously you must focus on Microsoft Certifications. To start with, you need to start with a single certification at a time. You cannot sail in multiple boats simultaneously. If you want to go for Cisco path then start preparing for CCNA and don't get distracted. First become expert in one domain and then when you are expert in one domain then exploring multiple domains.
All the best.

Government exams and the IT certifications you mentioned are different things. Understand the fact that government exams are aptitude based. You will have to prepare Maths, English and reasoning.
If you are preparing for government exams and in your spare time you think of doing these certifications then go for it. But, if you think that your certifications will help you in exams then it's a wrong notion.
Yes, you can go for government exams till the time you are eligible for them.

On the basis of experience, you can make a switch. If you want to switch from BPO industry to other industries, then it will be a bit difficult but it's possible. Starting as a software developer would not be recommended as you have already worked in industry for 6 years. You can do project management (PMP) certification and get into management. You can also look out for executive MBA programs. All the best.

Best MCSE certificate are:
*Microsoft Certified Solutions Expert (MCSE)
*Red Hat: RHCSA and RHCE. *Linux Professional Institute (LPI): LPIC System Administrator. *CompTIA Server+
*VMware Certified Professional Data Center Virtualization (VCP-DCV)
*Service Now Certified System Administrator.

It is the link to the page that will provide you with required info.
https://www.shiksha.com/it-software/course/amp/mcts-microsoft-certified-technical-specialist-athais-infotech-franchise-of-iiht-mulund-east-mumbai-178165

Follow the link below for details:
https://www.koenig-solutions.com/certification/mcse.aspx

You haven't told us about your previous background of education. But, as per industry trends I will suggest you to go with the MBA from a reputed institution and you can also go with MBA in Information Technology.