Degree

You can definitely do Degree in B.Sc or B.Tech. For that, you have to take admission on the Institute level seats offered by the universities. Best of luck for your future and if there's any query, feel free to ask.

Honors degree is having the dissertation process and normal degree can easily be achieve while honors degree cannot be easily achieved. I am attaching the link for clearing your doubts. Honors degree help one to get job easliy and in company also honors degree is preferred. Honors degree are meant to be more standard than a normal degree. http://www.differencebetween.net/miscellaneous/difference-between-bsc-and-bsc-hons/#ixzz48jR5nR97
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All the best.

As you rightly pointed, GATE is an entrance exam which is used by all central universities like IITs and NITs for M.Tech admission. Where as GRE is used for Masters admission in USA. You might also need to give TOEFL exams, some institutes need that too. But if you are looking for Masters in other countries (Canada/Australia/China/Hong Kong/Korea/ Japan) you might need to take IELTS along with the university specific test. It actually varies from country to country and course to course. If you have any country in mind and any specific course, can you please elaborate, so that we can help you better.
Best regards, Path.

B.Sc. (Computer Science) from Annamalai University (Distance Education), Tamil Nadu is a distance/correspondence degree offered by the institute. For further details regarding this course please refer to the link provided below:
https://www.shiksha.com/it-software/course/b-sc-computer-science-annamalai-university-distance-education-tamil-nadu-tamil-nadu-other-68354

B.Sc. (Computer Science) from Annamalai University (Distance Education), Tamil Nadu is a distance/correspondence degree offered by the institute. For further details regarding this course please refer to the link provided below. Regards.
https://www.shiksha.com/it-software/course/b-sc-computer-science-annamalai-university-distance-education-tamil-nadu-tamil-nadu-other-68354