^Yep. Pretty much sums up. & while some may argue that they are improving on points 1 & 2, No. 3 is still a huge issue.
You still haven't said whether you are ok with a smaller screen &/or older gen specs. For eg. you can get a Samsung Galaxy Trend for about Rs. 7.3k after discount, or a Lenovo a690, or a ZTE Blade C, or Huawei Ascend Y300 etc. etc. (if you are ok with last gen specs). One might debate that the latter brands are not top tier, but the general consensus is that they are far better than the Indian brands.
As for the usage, whether these specs are enough for gaming, it depends on what gaming you are into. These will run Temple Run & similar, but not Real Racing. (Iirc, a reviewer did show that the Galaxy Trend was fairly ok while running Dead Trigger - Just search geekyranjit on youtube). As for internet for PC via your phone, I really don't know & someone else should chime in about that.
Also, you could consider the Panasonic T11 if you're willing to stretch your budget & consider Panasonic to be a good brand. It's available for Rs. 8175 after discount on Indiatimes shopping. If
gsmarena is to be believed, it's got great specs for the price. (But I'd cross check before confirming. It could be inaccurate)
Edit:
This video seems to confirm the specs.
Edit #2: & if you are still going for the Xolo a500s, it's available for 5.6k on Indiatimes after discount.
HTH. Cheers!