When is a new block added to the bitcoin blockchain and is it vulnerable to modifications till then? I'm a beginner to Bitcoin and blockchain and from what I understand, one block can hold multiple transactions. Until a block is saturated with the number of transactions it will eventually hold, where are all these transactions stored? 
Until a transaction is added to a block whose hash is finally computed and the block added to the blockchain, how are the transactions tamperproof?
a block is assembled by the decision of a miner. If he wants to, he cannot include transactions at all. If he includes tx, then he uses tx out of his mempool. tx are normally verified before entering into a block. If the miner decides to tamper with a tx (change its contents), then when sending the block to the network, other nodes will reject this block, cause it contains an invalid tx.


  Until a transaction is added to a block ... how are the transactions tamperproof?


tx be tamperproof doesn't make sense, while the block is created. It is at the risk of the miner! If he wants to win the block reward, he better transmits correct blocks into the network. 
The whole idea of bitcoin is, to better play well and get incentivized for it. If you try to play against the network, you have enormous costs to carry.