MMS

You can get into following colleges based on your percentile in mumbai through maharashtra CET exam:
Vivekanand Education Society's Institute of Management Studies & Research, Mumbai
Alkesh Dinesh Modi Institute for Financial & Management Studies, Mumbai
Rizvi Institute of Management Studies & Research, Mumbai
Lala Lajpatrai Institute of Management, Mumbai
Zagdu Singh Charitable Trust's Thakur Institute of Management Studies & Research, Mumbai

Cut off at Bharat Vidyapeeth institute of management in round one is 99.39 percentile and in round 2, it is 99.22% percentile.

SIES COLLEGE OF ARTS, SCIENCE AND COMMERCE is a morning college and their class starts from 8:00 am to 3:00 pm and its same for the MMS degree.

The MHT CET Law cut offs are generally declared in four rounds of CAP Counselling based on closing marks. The cutoffs are released for the MH and OMS quota, which are further divided into Open, Open-EWS, SC, OBC, etc. categories. Candidates must note that the closing cut off marks are declared out of 150.

You can try but chances are low.Also you can explore about other colleges.

It is around 3.16 lakh.

According to the latest cutoff, you can get a seat in round one seat allocation with a 77.55 score at SRBS for Master of Management Studies (MMS), but in a later allocation.
According to the previous year's admission cut-off based on MAH CET for the Sheila Raheja School of Business Management & Research (SRBS), the cut-off percentile for the OBC category is 80.1 (OBCH) and 85.3 (OBCO).
Therefore, you are not eligible for admission in the first round for any specialization of the MMS course. However, you can get a seat allocation for admission in the later round. Therefore, you may wait for the Round 2 cutoff.

It is around 98%.

A Master in Management, or MIM, is a postgraduate programme that provides advanced general management knowledge for Business Bachelor's graduates, whether they have studied Business before or not. You will graduate a MIM programme with either a Master of Science (M.Sc) or a Master of Arts (M.A.) degree.
MSM programs are typically designed for students with less professional experience who want to develop business skills. MBA programs tend to require several years of professional work experience and are designed for business professionals looking to advance their careers.

The MMS term is used by the Maharastra State government for admission to the management colleges in Mumbai while MBA is a more generalised term used for management studies
And yes it comes under Mumbai University