Can two transactions, one spending the output of the other be broadcast to the network in close succession and end up in the same block?
yes
However, it is important to understand that (due to transaction malleability) the hash of the first transaction can be changed without your consent before it is confirmed. If this happens and the modified transaction is confirmed, then the second transaction will no longer be valid. It would need to be re-sent using the new transaction hash to define the input.
For this reason, it is generally not a good idea to spend bitcoins from unconfirmed transactions.
If this is true, then it is true for larger numbers of transactions?
yes
I.e. five transactions in the same block with four dependencies between them?
yes
Is there a limit for the number of transactions which can be mined per block in this way?
no, there is no such limit.
If the transaction hash is modified in any of the transactions in the chain of transactions, then all the transactions after it will become invalid and will all need to be re-sent.