Does my location really matter in my career growth, even working for the same company and at same salary? Would it matters in future?
Yes, and no. The most direct influence on your career is the work you are doing right now. The right location is the the location where you can do meaningful work, find good people to work with who can teach you and challenge you, and where you can learn new skills and technologies. Any job or location that does that is going to be better for your career than any job that doesn't.
It's usually hard to tell, without talking to people in a given company, what city is the best to live in for these sorts of opportunities. At first glance, it can seem like a big city, or a highly technical area, but in a given company, it could still be a smaller city, so long as the group and the projects they are working on are good. For example - in the US, there's a lot of great technology work in the smaller cities around New York, because New York is a very expensive place to host an engineering group.
One guideline is to know where the business is - often there are major laboratories, research centers, or development houses, where there are more opportunities. It may be connected to the corporate headquarters, but not necessarily. When I'm curious about this, I usually check the websites of the company and look for career positings and the products and services of each location, to see how much technical work the location offers and what they are making.
The other factor, of course, is other businesses in the area - which is worth checking similarly with job hunting in online postings to see if there's other work there in areas you'd be interested in working. Also, the presence of good schools and universities is a good sign.
Should I ask for the same salary when located in smaller areas as are given in large areas? That is, the expected salary in larger areas is greater than the normal expected salary in smaller areas.
You can try, but that would be unusual. Companies are usually quite sensitive to the pay rates in each location. When you're considering relocation, it is worthwhile to check the area to know what the cost of living will be. That'll tell you what salary will suit your needs. You can certainly aim high for any area if you get the option to quote a salary - but expect that the company will have a figure in mind and won't be interested in paying too much higher than the going rate for an engineer in that area.
One exception would be a corporate program where participants travel between locations, and where the salary is paid by a corporate standard that spans all the locations. Then it may be a negotiation against an abstract standard of the corporation, and where you choose to live will have a more direct affect on your standard of living, as the company won't change your rate if you move somewhere more expensive.