Colleges in Aurangabad

ME Part time (Electrical power system) is a three years of duration course at GECA with total intake of 13. Admission to these programs is based on GATE score and will be done through DTE Maharashtra website www.mahacet.org
The eligibility criteria is 50% aggregate marks at BE/B. Tech in relevant subjects. So, you have to apply through the DTE Maharashtra official website.

You should check this link:
https://www.shiksha.com/college-predictor

In counselling, mostly these steps are done:
These steps are done after registration, followed by choice fillup & call for reporting:-
1. Documents arrangement according to order, order list will be given at reporting center.
2. Carry all required original documents along with their photo copies and some photos (passport size) of yourself.
3. Document verification
4. They will give you a paper regarding the completion of counselling
5. Counselling over.

No, course cannot be done on part-time with any other course.
But, if you are referring for part time with job, you can do that. But, stills batch is not soft stone to crack.

You seem to have scored quite well. I think you will be able to make it to the open category.

You can use this superb tool to compare both these colleges:
https://www.shiksha.com/resources/college-comparison

Here are some government colleges in Madhya Pradesh:
1- Government Engineering College (Rewa)
2-Ujjain Engineering College
3- Jabalpur Engineering College
4- Government. Madhav Science College
5-Government Arts and Commerce Naveen College
6- Home Science College
7-Indira Gandhi Engineering College
8- Dr. Bhagwat Sahay Government College