M.Arch

Placements in architecture, though they exist still are pretty rare. So, mostly 'No'.
You need to apply directly to the firms that you want to work with and hope that you get an interview call and if everything goes well, you'll be able to grab the desired job.
Nowadays, most universities are having some form of placements, they are still in their infancy and hardly two or three companies will come looking for candidates. In most cases, these companies will be project management companies such as L&T or large scale developers such as Sobha builders.
As a fresher, it may not always be a good idea to join such large-scale offices because you might miss out on learning the basics of architecture and construction.
In any case, make sure you are understanding the kind of job profile these companies offer before signing up for any kind of campus placement.

This completely depends on you, though there are ample amount of job opportunities after M.Arch, but if you go for higher studies you are definitely adding and expanding your knowledge and scope. It is always good and helpful, if you have more knowledge and higher degrees. NIT depends completely on you and your circumstances, if you want to pursue higher studies or start working. If you have enough time and money to go for higher studies, I'll suggest you to go for higher studies, rest is your choice. I am explaining below what are career prospects after M.arch and what you can pursue in higher studies:
M.Arch graduate can acquire a career in both private and public sector. After M.Arch, there are numerous job opportunities for post graduates in M.Arch in private sector. They can get jobs in construction companies and they can work as an architectural consultant in those companies. There are many companies in our country which offer good profile for an M.Arch degree holder. Some of those companies are:
DLF
L&T
Sahara Group
Eros Group
Many of the private institutions also recruit M.Arch graduates for the teaching jobs. If a candidate is interested in this profession, then he / she can find a job in this sector. M.Arch degree holder can work as:
Art Director
Technical Illustrator
Architectural Historian/Journalist
Building Contractor
Interior Designer
Architectural Engineer
Building Researcher
Landscape Architect
Set Designer
Building Inspector
Government Career after M.Arch:
For M. Arch holders, there are a number of opportunities in the government sector. Many changes have been happening in the architectural field. A candidate has equal number of opportunities in government sector and in the private sector. Some of the opportunities are in the following sectors:
Municipalities
Central and State Public Work Departments
Housing Development Corporations
Public Works Department (PWD) urban Development Corporations
State Housing Boards
Post and Telegraph
Town and Country Planning organisation
Department Of Railways
National Institutes of Urban Affairs and Housing
National Building organisation
City Development Authorities
Candidates also opt for teaching profession after the post-graduation in architecture. The salary scale for lecturer is very high. More candidates are attracted towards the government sector because of the job security and reputation. But, candidates can only acquire these jobs after successfully clearing the written exam.