What are the actual anonymity features of ZCash? I have looked at their FAQ but I didn't find the answer to this.

Having looked at their whitepaper, it seems to me that the main feature of ZCash is that you can't trace where the money came from, because of zero-knowledge proofs.

My question is, does ZCash also feature anonymity the other way – not being able to trace who the money was paid TO, after it has been paid?

In other words, someone lost X amount, someone gained X amount, and we can't prove who paid whom. But what about simply finding all the people in that block who either gained or lost X? Zcash says it "does not: ... protect against correlations made with public transaction" but what about internal transaction?
As a short answer, yes you can have a transaction that does not allow others to trace who the money was paid. 

Zcash supports four kinds of transactions that are categorized as follows, 


Public-address to Public-address (like as the ones in Bitcoin)
Public-address to Private-address (they call it shielded transactions)
Private-address to Public-address (they call it deshielded transactions)
Private-address to Private-address (they call it shielded pool transactions)


For transactions in Shielded Pool, origin, amount and destination are anonymous, but in deshielded or shielded transactions only one side is hidden. Recently there was an empirical analysis of anonymity in Zcash that has some very interesting result. I highlight some of them here, 


Only 0.3% of Zcash transactions are done in shielded pools (the transactions that are completely anonymous) and only 14.96% of transactions do interact with shielded pools.
73.5% of Zcash users only use public transactions that already exist in Bitcoin and are shown to be linkable.
Only 25% of visible addresses have a non-zero balance, and more surprisingly the top 1% hold 78% of all Zcash coins (ZEC).  
Founders of Zcash behavior with quite obvious patterns that make easy to trace their transactions. e. g. analysis show that 14 addresses of founders had been used regularly  to deposit coins to the pools.


You may read more details on https://arxiv.org/abs/1805.03180