Is transaction time correlated to block generation time As I unterstood in other answers (see https://bitcoin.stackexchange.com/a/8922/74399), a transaction is added to the blockchain, once a new block has been found/generated. 
The average time between two blocks is about 8 minutes regarding the past 24 hours.

Does this mean, that my transaction will take an average of 8 minutes to become visible in the blockchain?
Is it known in the network as an "unconfirmed transaction" (so it's save)?
On average, based on Bitcoin protocol, a block takes 10 minutes to mine.  Transactions that optimize miner profit take precedence in the block. In other words, the transactions that pay the highest fee get incorporated into the block first and therefore get confirmed the fastest since currently the mempool is large. The mempool consists of all transactions that are waiting to be mined into a block. A transaction that pays a low fee can be stuck in the mempool for a very long time if the mempool remains crowded, so it’s hard to say how long a particular transaction can take; but, yes, a transaction that is broadcast to the network remains unconfirmed until mined into the blockchain.