UK

The country in question is the issue here as getting a work permit for Indian students is very difficult. Now, which course you should do is entirely your choice. By now, you should figure out your plans. What type of job do you want is something you should ask yourself and accordingly pick. If there is no work experience, then I will suggest apply for work or gain solid experience in India. If you want to another MBA programme you will need work experience. If you want to do a Masters in sales or marketing then again you already have an MBA. It's not going to be easy. Digital Marketing, Data Analytics are some you can see. These are in demand.

Yes, PCM students can go for London School of Economics as far as I know. There are some exams that you need to clear before you get into London School of Economics. But I would suggest for graduation you should be in India. Choose the best institution in India if you think your marks of good like ST. Stephen's College or Indian Statistical Institute which are very good colleges for economics honours and after doing your graduation, go for London School of Economics for Master's degree. But the final decision is completely yours. Please check the college website of London School of Economics. There you will find a link to request the brochure.

It completely depends on you, because there are several aspects which are to be considered for deciding that where you should pursue your degree in India or abroad. So let's start
Fees: affordable and cheap at several places in India but extremely high abroad and will become even more after adding all accommodation costs. Course structure:well updated and a type of tailor made for students different specialisations and world class teaching technology, but India mostly the same curriculum everywhere except a difference of 20-25% in the programme. Duration: BBA in India is a 3 year degree course but mostly abroad it is a 4 year degree, so will be getting an extra year which will give you more knowledge. But in India also several institutions are providing world class education. Placements: there is nothing like on campus placement abroad but you will be given some time to find a job after you finish your degree but that is so hard. But here in India there are several universities or colleges which provides good course and placements for BBA and you can get easily a job of 15-20k per month. Some good colleges in terms of placements, teaching faculty, placements etc. Are:
1, Christ University Bangalore
2, Delhi University
3, GGSIPU
4, Amity Noida
5, kj Somaiya Mumbai
6, Madras Christian college
There are several others also. These were the some most common things to consider well there are more but according to your query I think these are enough. Best of luck for your future.