LBS vs LSE Masters for London IB/PE

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1. Then GPA shouldn't be an issue for you so long as you manage a GRE score higher than 330 (for LBS), but scholarships are going to be hard because we're an overrepresented demographic and GRE scores don't allow you to differentiate yourself unlike GMAT ones. Again, your work ex would impress LBS, that's not an issue; the problem is with recruiting. Recruiters there won't recognise any IB work ex in India that's not from a well-known BB. 
2. As for the LBS MFA employment report, I don't know what job functions are categorised under IB for the purpose of their classification. I recommend talking to international students from Asia who're currently enrolled in the program. I talked to 20-25 of them (mostly Asians/Non-Europeans ) and the general sense I got was that most of the East/SE Asians that got front-end IB roles post grad in the last cycle did so in their home countries or the APAC region (China, Singapore, Hong Kong, etc). For the Indians I talked to, 2 of them are working in Mumbai, 1 in the Middle East and 3 were in middle/back office grad roles. 
3. As for HEC, I'm not sure what the visa issues are. Work visas in the EU aren't a problem, it's the language as you said. Most non-European language speakers that attend HEC's MIF also end up trying to recruit for London or their homes countries again. It can be worth applying to if it ends up being significantly cheaper than LSE/LBS and if you're doing the longer program (2 years+) because the bigger firms in the UK aren't filtering on the basis of whether or not you have the PSW for 18 months post graduation.