You can surely invest in cryptocurrencies from India. Cryptos in India are in a grey area right now. That is they are neither banned nor legal. So in the worst case scenario crypto exchanges operating in India can be closed, nothing more. If you have funds in non Indian crypto exchanges, then no issue at all.
To invest in cryptocurrency from India, you will first need to buy Bitcoin. You can do so via Indian exchanges like Unocoin, Zebpay etc. Or you can try localbitcoin.com site, where you can buy Bitcoin from another person. But do know there is a big risk involved in this way. You could be scammed by a trader and the prices are usually higher than the market price. So exchanges are the safest options.
After you buy your Bitcoins, it's better to transfer them to wallets like coinbase, Xapo etc. After that you can easily buy other cryptos like Ether, Ripple, Litecoin etc. from exchanges like Poloniex, Openledger etc.
Hope this helps you to enter into the crypto world. 😊
Agree with all of your points. There is a certain degree of risk associated with investing into the crypto world and this applies to any country in the world. Scammers and cheaters will try to scam you whenever possible which is why the op needs to do a good deal of research before investing into specific crypto. Personally, I prefer using Zebpay and I love this wallet due to the speed at which my transactions are processed and since it is highly secure. Do your research op.