IES

Yes, you can in fact clear IES Mains exam with CSE branch but you have to focus on another branch's subjects and clear the IES exam.

Diploma holder students are not eligible to apply for NITs. You can appear for JEE Main exam to be eligible for JEE Advanced exam. You can take admission in IITs but in 1st year of engineering.

For this, the eligibility is that you should hold a graduate degree in engineering. You should be a B.Tech only then you can fill for the job.

https://www.onlineengineersacademy.org/ese/
another one is byju's you can join classes.

As per UPSC, any government official applying for IES/ ESE will get the age relaxation even if he/she is already working on a post which is considered of a higher officer cadre. There is an age relaxation for the ones who have worked with any government organisation on contractual basis for a period of 3 years or more.

Yes, anyone can apply what matters is your graduation.

Yes, you can apply for the exam.

If you are preparing for GATE, then study with made easy materials.

There are many government exams to be conducted. 1st SSC CGL last date of form submission 25th November 19, Madhya Pradesh PSC state service exam form submission 20th nov to 9th dec 19. RRB NTPC etc. And UPSC CSE 2020.