SRM Institute of Science and Technology, Kattankulathur

Yes, it is a very good option.

You must have to appear the VITEEE 2019 SRMEEE 2019 EXAM, there is no connection with JEE.
Without exam clearance, you are not eligible to get admission.

You can get admission in almost all private colleges through the management quota seat. You are asking about SRM and Manipal. Manipal is more costly than SRM.

As we all know, SRM University is well known for its placements. As far as CSE department is concerned, the placement ratio is almost 75%. The average salary package goes around 4 to 5 LPA. And the highest around 25-30 LPA. But the package someone is offered, also depends on performance during the interview. For better understanding, click the link:
https://www.shiksha.com/university/srm-institute-of-science-and-technology-kattankulathur-chennai-24749

JB, SRM Guntur (Andhra Pradesh) is a new campus of SRM University and first batch will pass out in year 2021. While SRM Chennai campus is an old campus and established in 1985, and have very good record of placement. So, you should go with SRM Chennai campus.

Give SRMCET or if you can't crack it then go for management quota. It's not tough to get a seat in SRM.

As both colleges are good enough. But, if you want to choose one of them, I would recommend you to choose VITEEE, as your first preference, because it has good faculty members, good facilities, well infrastructure etc. And, last but not the least good placement.

As you said, it has branches in many states but SRM campus Potheri Kattankulathur is the best as per my knowledge. It is the main campus of SRM. Even placements also take place in this campus. No matter in which campus you are, for placement you have to come to main campus. Infrastructure wise also main campus is good but I heard Amravati campus might be better in terms of infrastructure.

Yes, you can seek the course, if you get very good marks and ranking in Your JEE exams. And, have to be at least in 1000-10000 rank. All the best.