Blochchains that support data privacy and/or strengthen parties pseudonymity Question  1:  Is there any blockchain that allows users to store their private data in the chain? For instance, the transactions and amount of Bitcoin one has is hidden from others. 

Question  2: Is there any blockchain that strengthens participants pseudonymity? so it won't be very easy to associate an owner of ID/transaction to a real person.

In terms of question 1, I'm aware that hyperledger does it, but the problem with this framework is that data and blockchain are encrypted using a single key and this key is distributed among the participants, but I think it's 
not a sophisticated approach. 

In terms of question 2, I've heard that there's a blockchain (I think it's called Zikas) that somehow mixes transactiontors but I'm not sure about it.
For question 1 and 2, ZCash (not Zikas) provides some solutions.
It's based on Bitcoin's code and has 2 types of addresses:


non-shielded: they behave exactly like normal Bitcoin addresses
shielded: you can't know how much they are transacting nor to whom they're sending funds (unless it's to non shielded addresses).


If you only use shielded addresses, and only send funds to shielded addresses, it's impossible (just from looking at the blockchain) to know how much zcash you have, nor with whom you're transacting with. However, creating shielded transactions is slow (it takes minutes IIRC), and your wallet has to scan the full blockchain to know if you've received payments.

OTOH, shielded transactions give you the possibility to attach a custom memo to them which will be private between you and the recipient.