Which is better: Invest my Bitcoin on legit mining sites and purchased power before the halving because it is currently cheap or save my bitcoin and trade it after the halving because its value might be doubled?
In my opinion if you make Investment on cloud mining service, it will give pasive income and will need much time until return of investment. But if you buy bitcoin today bitcoin's price is still high, if you want buy bitcoin wait until month November. So depend on your choice, for me trading altcoins is more better than investing on cloud mining and save bitcoin.
Why November? Is this related to halving thing or something like that? Is something unusual will happen on November?

Anyways yes, altcoin trading is much better than investing in cloudmining. Both have high risk but you can play along with altcoin trading while on cloudmining you will just have to wait if they will pay you or not.