Diploma

Yes, definitely you can go for Diploma after class 10th, which will be of your duration 3 years. You are class 10th, pass out of 2013. So, you will have to provide a gap certificate while taking admission. There are many options available for Diploma in engineering and you can choose as per your int

Yes, it is required by the companies in India and Abroad.

Yes, it is highly demanded programme and accepted in the industry for technical jobs.

Yes, they provide one year Diploma certificate. These are job oriented courses are very helpful to get into the industry asap.

Check out this link: http://mitcoe.ac.in/wp-content/uploads/download/03_admission/06_cut-off/Direct-Second-Year-2016-2017-Cut-off-list.pdf

Both the options are good and followed by many students. By dropping, you will only able to clear intermediate exam. But if you go for Diploma in computer Science and work hard, then after one year, you will have only two years to get Diploma certificate. So you can get a job also with Diploma. So,

Hi Vijay,
Yes, you can get admission via lateral entry. You are eligible. Those students, who will join through lateral entry will get admission in second year directly.
Best of luck.