MHT CET

Yes, you do require a domicile, even though you have done all your basic education in Maharashtra. It will take only 10 to 15 days. You can approach an agent, but they will charge around Rs.6000. It is better to do it yourself and everything will get over within Rs.50 to Rs.100.

MHCET will take above 60% in HSC but your admission will be depend on the MHCET exam score. So, focus more on that.
Good luck.

MH-CET form deadline was extended from 11th March till 18th March. So, I doubt if you can fill the form now. The test is conducted by Maharashtra Government's State Common Entrance Test Cell you can check out their website for further information. Following is Test Cell's address and contact:
State CET Cell, Maharashtra State, Mumbai.
8th Floor, New Excelsior Building, A. K. Nayak Marg, Fort, Mumbai- 400 001. Tel: 022 22016157 / 59/ 53/ 34/ 19/ 28
website: http://cetcell.mahacet.org/.

Refer to the link below and download the papers:
https://www.shiksha.com/b-tech/mht-cet-exam-question-papers.

MHT CET 2019 is scheduled on multiple dates from May 2 to May 13. Once you get your admit card, which will be released on April 25, 2019, you will get to know your exact examination date of MHT CET. Since on the admit card it is written.

The issue date of admit card is in month of April, then only will get to know where will be center of exam.

Please refer the link below for MHT CET syllabus:
https://www.shiksha.com/b-tech/mht-cet-exam-syllabus.

Yes, please refer https://www.shiksha.com/b-tech/mht-cet-exam-question-papers.