Engineering Entrance Exam

No, the scores of MHCET and JEE Mains do not matter to take admission for B.Sc in Mumbai University.

According to me, you should not drop instead opt a good college that you can get according to your rank and then in that college maintain yourself in top position.

Hello,
143 is a fair score and you can take up computers from other colleges than IITs. You can also opt for other private colleges for a better score and better choice for the degree.

Last time revision for JEE Advanced should comprise more of tests. Also, try to look at important formulas and concepts. Do have a sheet with formulas. Tests will make you more comfortable with strong topics and will let you know the weaker topics. There will be some extremely difficult questions, difficult to solve so better focus on strong topics.

Please check for your eligibility to appear for the GATE exams from the criteria mentioned below. GATE 2017 Eligibility: https://www.shiksha.com/engineering/articles/gate-2017-eligibility-exam-centers-blogId-12868
For further details regarding the GATE exam like important dates, exam pattern, question papers, syllabus etc. Please refer to the link provided below:
https://www.shiksha.com/engineering/exams/gate.

140+ is a safe score for getting admission in PICT, Pune through JEE Mains entrance exam to do BE Information Technology.

Clarify your category first. If you are from general category then it is a little bit tough to get a government college. Other than general category, there is a possibility of getting a government college.

Yes, definitely. Hope you meet the cut-off criteria as required.
Best regards.

Go through the related websites and search in either examination or downloads section. You'll find previous year papers and sample papers for sure.