I'll share my recent experience in Delhi at Chanakya Mall if it helps anyone else. To note, it's a significantly smaller store than Mumbai, but I chose Delhi since I wanted to B hunt, and even if the inventory was better, I didn't want to be shopping in Mumbai during its annual Lakme fashion week.
First, prices are about 10% higher than in the US, but this is actually less than it was since India streamlined its tax structure and reduced luxury goods from 28% tax slab to 15%. On some of the pricetags you can literally see a reduction since the switch.
Inventory: Lots of good stuff, esp for bag lovers. I saw everything except B/K/Cs, including bolides, Evelyns, toolboxes, Lindys, etc. The colors were classy and generally neutral. I also saw a gorgeous Kelly wallet in gold, as well as a Bearn in ostrich--couldn't pinpoint the yellow/beige hue on it but it was stunning. I was a little disappointed in shoes since the stock there was kinda meh. I was looking for either jumping boots or the neo kelly boots, but had to "settle" for the power low boots. Makes sense that stock in August for these would be limited, though. Twilly selection was great, scarves were okay, and home goods were also on the limited side (probably because this section--along with dishware and fine porcelain--is one of the least popular selling items in India).
The big "can I get a B/K/C" question: I live in a different state in India with no H store, so I technically qualify as a resident. My husband is Indian and I'm white, and we both went shopping together on a Tuesday early afternoon. Based on what others said I don't know if foreigners/non-residents can get one unless they drop serious money in one sitting. That said... we dropped about 4.5k (USD) on several different things from several depts. Maybe that's not much in the H world, but I thought it'd at least get my foot in the door. Yet, when expressing my interest in getting a Birkin (only post-checkout of course), they didn't so much ask what kind I was looking for. I would've even welcomed something like, "how long are you in town for? Come back and see us later" (ie, just shop more and we'll talk). Instead... uncomfortable silence on the matter. And I mean, NO reception. This was despite great rapport otherwise. Though the SAs are absolutely lovely and not at all snobby, on the topic of the B I got the distinct impression that they wanted me to ask about anything BUT that. It was like doing really well in a job interview but coming away from it getting the impression that the position was filled already and there wasn't anything you could do to change it. On the way out I asked, "uh, is there a waitlist, do I need to sign any form, or...?" I got a, "well, we have your info so we'll call you if anything comes up." It's only been 2 days since my visit but I came away thinking it might as well be two years and I think I'd still be waiting. I'll of course update if I get an offer and the amount of time it took, but that may be a while! In the meantime I'll enjoy my lovely purchases.