Degree

No, you can't apply for admission in any MBA college with having one backlog. No college permits the seat, if you have backlogs.
First of all, clear your backlog before the completion of your BBM, then apply for the admission in various colleges. And to apply for MBA you must have good percent in degree and you should write the exams like CAT, MAT etc.
No age limits are there in MBA. You can select any stream, as you like Marketing, HR, Finance, Telecom etc.
Typical exam pattern of MBA includes;
Quantitative Aptitude
Reading Comprehension
Verbal Ability
Data Interpretation
Reasoning
Data Sufficiency
And, you can do the MBA in many ways like
Part time MBA
Full time MBA
E MBA and online MBA

Your question covers an entire industry. Aviation sector is huge and has a lot of job profiles related to it. It depends on you where you want to go. Please clarify so that I can respond accordingly.
That is a question asked about the industry and there is no mention of the job profile.
Such questions require discussion as they look to elaborate an industry and not just a profile.
I'll give you a brief about the main job portfolios that are hosted by the aviation industry:
For Pilot Training:
1. Indira Gandhi Rashtriya Udan Academy (IGRUA) - Rae Bareli is the only government-owned institute for pilot training.
There are state flying clubs which run in collaboration with state governments:
2. Madhya Pradesh Flying Club - Indore & Bhopal
3. Nagpur Flying Club, etc.
CAE Gondia is another premier institute which works in collaboration with some private airlines to train candidates to obtain a CPL.
For AME (Aircraft Maintenance Engineer) Course:
1. Indian Institute Of Aeronautics (IIA)
2. Indian Aviation Academy
For Flight Dispatchers Course:
1. CTE Hyderabad - Run by Air India
For air hostess training:
There are no government-owned colleges. However, a number of private academies are operational in the market.
This was an explanation that basically covers wider view about the main job roles in aviation industry, choose yours wisely and then proceed accordingly.

Hi Souvik, admission has already commenced for B.Sc+ M.Sc Integrated course in multimedia. You can apply for admission only if your results are out. If you are an ISC candidate I suppose you can apply for it right away.
I will provide you with few links which might help you with your admission:-
1) Link for information about admission: http://www.sxccal.edu/admissions/SXCAdmission2018/UG8102/default.htm,
2) Link to online application: https://sxcadmissions.in/xavadm8102/default2018.asp,
3) Eligibility criteria: http://www.sxccal.edu/admissions/SXCAdmission2018/UG8102/EligibilityCriteria.htm,
4) College fees: http://www.sxccal.edu/admissions/SXCAdmission2018/UG8102/fees.htm.
Kindly check all the links. Hope to see you in Xavier's soon.
Wishing you good luck!
Revert back in case you face any doubt.