Which types of online trades are haram? I would like to know under which basis trading for stocks, and similar types of trading are haram.
You should try to, if you are going to trade, avoid risks. If you are pretty certain, then I do not see why it is 'haraam'. If you are not certain, then it is like gambling, which IS haraam.
Forex trading is the trading of currencies. Again, I would look to the prior advice. If you are not certain that you would gain, do not do it as it would be counted as gambling.
Options trading is gambling. There isn't really a way to see it as halal. It honestly is just a person saying thy will sell something in the future at this price, or buy something in the future at this price. It is gambling.
Cryptocurrencies are digital currencies. Saying that thy on their own is haram is like saying that the US dollar, the Euro and the GBP is haram, it's not. Its what you do with them that is halal/haraam, likewise for most things. They become haraam with your intention on what to do with them. If you see it as a more secure way to store money, or a good way to pay online for things, then that is halal. If you would like to gamble with it, or loan off with interest, that is haraam.
I am NO scholar. I am infact a recent convert/someone who became more religious in the past month or two. I am only saying things based off of my view/interpretation of the Hadith, Quran and Sunnah.