Do Private colleges participate in CSAB Counselling?

Yeah you can get ECE in NIT Mizoram and EEE in NIT Nagaland, and CSE in IIIT Manipur. The best option I can recommend here is ECE from NIT Mizoram.

Yes but it is a rare chance to get CSE with 3 lack general rank because there is only few left government colleges are got to students after Jossa councelling with rank under 1lack ( general)

Candidates who have passed their class 12th (or equivalent) with the required subjects and have a valid rank in either JEE Main 2025 or JEE Advanced 2025 are eligible to participate in the JoSAA counselling. Generally, Physics, Chemistry, and Mathematics are the compulsory subjects for Class 12th. 

To be eligible to participate in the CSAB, candidates must have a valid JEE Main rank, have participated in the JoSAA counselling, but were not allotted a seat, did not accept the seat or cancelled it. 

Joint Seat Allocation Authority (JoSAA) is an authority to manage and conduct the entire seat allocation process for IITs, NITs, IIITs, and other Government Funded Technical Institutes (GFTIs). JoSAA considers JEE (Main and Advanced) to participate in the seat allocation process. On the other hand, the Central Seat Allocation Board (CSAB) is an authority responsible for conducting the process of seat allocation for undergraduate engineering, technology and architecture programs in the NITs, IIEST, IIITs, SPAs and GFTIs (collectively known as NIT + system).