CAT

As per my knowledge, direct admission without entrance exam is offered by few Private Universities. However, it is not possible to get direct admission even if it's for Executive MBA in the top colleges without entrance exam some of the best colleges with executive PG courses are Indian Business School Hyderabad, FMS Delhi and all the IIMS and IITs. So, don't be misguided, if you want to go for a post-graduation programme, do look into these colleges' eligibility, their academic course structure and prepare for the entrance tests. All the best.

Yes, you can join IIM after completing your graduation. To get admission in IIM your CAT scores should be more like 99percentile after that u will need to crack their GDPI rounds and they will also check your class 10th, class 12th and graduation scores you need to pass all this test and they will also check your work experience.

You can have your German Language Diploma from following famous colleges such as Allahabad State University, Bharti College in Delhi, Guru Ghasidas Vishwavidyalaya.

You must choose according to your interest. Prepare well and still if you don't succeed, then you can do MA from Economics. It's an excellent subject and has lots of scope.

Registration starts from August and ends in September for CAT 2019 and exam will held in November, but it's not possible to get admission this year so you have to wait for next year.

To get FMS, Delhi you should have 95 percentile at least and after CAT FMS take their own test. To get admission here you have to perform well in both CAT as well as FMS test.
Good luck.

Yes, after graduation you can do CAT. You can take CAT exam in your final year of graduation. You will be eligible for that. Good luck.

Here is the complete admission process to get into this university, you can follow the link:
https://www.shiksha.com/university/amity-university-Noida-41334/admission

You need to appear for the CUSAT examination.
You can get detailed information about it from this link:
https://www.shiksha.com/university/cusat-cochin-university-of-science-and-technology-kochi-28013/admission
Best of luck.