Polytechnic

Yes, you can. Many countries and colleges will allow you to apply for B.Tech, but some colleges will allow you to apply for advanced diplomas or so. So, you should start checking college's websites for the requirements and email them also.

My friend, you have many options!
1. B.Tech/B.E
2. NDA (if you are interested in army)
If you want to do job then many organisation and even PSU's offer recruitment for Polytechnic student. Like BHAIL, NTPC, BPCL etc. For any further doubts or query, feel free to ask.
Best of luck.

No, IIT does not take admission after 3 years since IIT does not provide lateral entry and hence you can't get admission in IIT IIIT, etc. You can get admission in lateral entry in private colleges.

Yes, you can pursue B.Tech in mechanical engineering. You need to appear for the lateral entry entrance exam.

B.Tech/BE through distance will be the best for you as you already have 6 years of work experience. Distance B.Tech degree along with your work experience will prove beneficial for you in the future.

You will get admission in DTU through LEET only when you process the 3-year Diploma result in front of DTU LEET committee.

Hello Atharva,
If you intend to get admission in an IIT then the answer is yes. This is so since IIT's treat Diploma as equivalent to 12th and hence you can appear for JEE Mains and JEE Advanced for admission. However, if your intention is for lateral admission then you will have to go through matrix of eligibility versus possible branches of engineering, available on website of DTE of Tech Edu Maharashtra.