When you say "low electricity" what do mean?

Plug in your information and see for yourself what the costs will be and any potential profits will be with a mining calculator.
http://www.coinwarz.com/calculators/bitcoin-mining-calculator

You may want to check out a few different calculators. Some give you more/better information than others. Combined, they will give you the big picture.

The speed of your internet connection is inconsequential. Mining is not internet intensive. Just need a stable internet connection.
Air conditioning may not be the issue. AC will be fine to cool off the room, but you REALLY need a way to vent the heat outside of the room. That is one of the most important, IMHO.

Not a good idear... Basically, to have a chance of turning a profit, you'll need to invest in ASIC's and have very cheap power (and even then, it's very hard to make a profit).
You could use your VPS to manage your ASIC's, but that's basically it. But instead of using a VPS, you could use an old pc, laptop, raspberry pi,... to achieve the same task... In the end, it'll be cheaper than using a VPS, and it will save you a lot of routing/firewall/DNS/... related problems since you can run this raspberry (pc/laptop) in the same network as your ASIC.