Ofcourse you can short bitcoin. You can short sell anything that moves, including cryptocurrencies. You can borrow bitcoin at a rate you agree and just sell it with the hopes that price will decline if not then you're burned plus you have to pay the lending rates. Personally I never trade with leverages although it is very tempting, it's just, I can't absorb the risk that entails. You can short as well without borrowing, yes you can always make money when prices goes down.
In my opinion you only diversify when you don't know what you're doing and you have a lot of capital to diversify. When you only have - let's say below 100k php. For me, it is better stick into 1 or 2 cryptocurrencies/projects you believe in and ofcourse assuming you did your due diligence on those projects.
Have not seen any exchanges yet that offer short selling..
I agree on not to diversify on your cryptocurrency investment(you could do it in stocks) if there will be a specific metrics to value the coin that you choice, the problem is we know it that cryptocurrency is the future, its just we don't know which one will become more dominant in the future..