IIM

Yes. To some extent. They do give you some extra points if you have some years of work experience. But you need to have atleast 2 years of work experience for that. Anything less than that will be of no use. And anything above 4 years is also of no use.
But again with awesome CAT percentile and good profile you can still get a call for GDPI with no experience.
Good luck.

Yes, you are eligible for the same.

Yes, indeed, you are eligible, but try to score above 99 percentile in CAT for old IIMs and 97 percentile for new IIMs.

If money is a constraint, then FMS is the best solution for this problem. Though loans are easily available in the market on the name of IIMs. However, I do agree with your point that loans can be burdensome on you as well as your parents. Hence, if you are not willing to spend much money into MBA, then FMS is the college for you.

First of all, every college is good. Be it IIM or FMS, every college has its own merits and demerits. Hence, it becomes more of a personal choice on which college to select.
However, according to my personal opinion, if you are interested in marketing then FMS is the college for you and if you finance focused, then concentrate on IIMs, especially IIM Calcutta.

Firstly, register for an exam called CAT. Know its syllabus, and start studying for it. 4-5 months of dedicated preparation is enough to crack the exam. It will be held in November 2017. Post the exam, start preparing for the interviews. If you clear the cutoffs of various IIMs (around 99 percentile), then you will be notified about it. Then, appear for the interview rounds (usually held in February) and perform well. If you clear the interviews, you'll be given admission for the respective IIMs.

Admission in IIMs is based on Combined Admission Test (CAT) conducted by IIMs. The eligibility criteria for appearing in CAT is Bachelors degree in any discipline from a recognised university with aggregate marks of 50% or above. CAT 2016 will be held on 04 December for MBA 2017-19 batch. You cannot apply for it now. Advertisement for CAT is generally published in August in leading newspapers. You may appear for CAT 2017.

You can do, provided you comply with the requirements of those short-term courses. One of the main parameters is relevant work experience for certain number of years. These are advertised by IIM/s. So, keep a watch on those.