MBA/PGDM

There is no age limit or restriction for pursuing MBA however there is no point on doing MBA if you cannot make into top 50 institutes as it makes virtually impossible to get a job. Second, you need to justify for your age and gap in education also. So plan accordingly. If you don't get into top 50 institutes then join a job, gain some experience and do a part time MBA from a good, well reputed institute.

If you are planning for a PGDM do only 2 years full time program and check whether it has approval from AICTE and whether AIU has granted it equivalency status of an MBA program. Whether PGDM or MBA opt it from top 50 institute only and if you don't make it, opt for a part time MBA program.

Yes, you are eligible but before doing PG Diploma you should join a job as materials management executive or store executive or purchase executive or distribution executive either in a corporate 3rd party logistic company or corporate.You may do a PG Diploma from Indian Institute of Materials Management and also from Directorate of Distance Education, Annamalai University.

You should prefer business management as hospitality management has limited opportunity. You may find career opportunity with hospital and aviation sector in various departments in operational role.

You should consider taking a student loan provided by SBI or other banks.

The eligibility for MBA in Information Technology will be having Bachelors Degree in Information Technology, Computer Science and a 50 per cent passing score in CAT / GMAT/ other management exams. Some colleges will also prefer a two to three months Working Experience.
There is a rich demand of IT professionals having expertise in business management in the market today. Also they are very well paid.

If your target is MBA then courses mentioned by you may not add value to your career. You are advised to join an NGO during summer vacations to build your leadership skills which will help you to be a good leader after MBA.