Government Polytechnic Pune

The first step to apply for a college is to fill the admission form. you may collect the same from the institute.

Yes, you can. here is the list of colleges for external admission in engineering department:
Indira Gandhi National Open University (1985)
Dr. B. R. Ambedkar Open University (1982)
Kotak Open University (1987)
Nalanda Open University (1987)
Yashwantrao Chavan Maharashtra Open University (1989)
Madhya Pradesh Bhoj (Open) University (1991)
Dr. Babasaheb Ambedkar Open University (1994)
Karnataka State Open University (1996)
Netaji Subhas Open University (1997).

76% is the cut-off for civil engineering.

Government Polytechnic, Pune is better than Nashik. Pune has good placement records than Nashik. Pune has 2.5 lacs per annum average placement rate whereas Nashik has lower.

Admission is through Centralized Admission Process of DTE Maharashtra based on marks obtained in class 10th. Hence, I will advise to appear for the counselling first, and then decide.
Details below:
https://www.shiksha.com/engineering/course/diploma-in-computer-engineering-government-polytechnic-pune-shivaji-nagar-275292

You need to have minimum 35% marks in class 10th, and also must have passed Mathematics and Science subjects.

Admission is through Centralised Admission Process of Maharashtra based on marks obtained in 10th class.
Details below ;
https://www.shiksha.com/engineering/course/diploma-in-civil-engineering-government-polytechnic-pune-shivaji-nagar-275288

Admission is through Centralised Admission Process of Maharashtra based on marks obtained in 10th class.
Details below:
https://www.shiksha.com/engineering/course/diploma-in-civil-engineering-government-polytechnic-pune-shivaji-nagar-275288