In the case the difficulty increases as much in future, will the possible hashes run out/be insecure? As I understood, in the block hash, the amount of zero's is the nonce, like this:

0000000000000000005f54622d97866453137466737289c2500e67f6fce1cd4e


When there are more blocks found than in the average of 10 minutes, the nonce will increase. Then the hash is recomputed for each value until a hash containing the required number of zero bits is found.

But imagine the development of ASIC's accerlates expotentially, so the nonce for the required hash will be like this, for example:

000000000000000000000000000000000000000000000000000000000000004e


I know there are more information required, but let's imagine this in 2020 if the development of new ASIC could accelerate. 

So in theory there are only 28 (note the position of 4 in block hash) x 28 (position of e in block hash) = 784 remaining possible hashes. Would thatn't mean that the Bitcoin ecosystem with an insane difficulty will eventually runs out of possible hash combinations for blocks?
As I understood, in the block hash, the amount of zero's is the nonce,


No, that is incorrect.

The nonce is a value in the block header, which is then hashed. By changing the nonce, a new block header is effectively created which has its own unique hash.


  Then the hash is recomputed for each value until a hash containing the required number of zero bits is found.


No. Contrary to popular belief, the correct hash is not based on the number of zeros in the block hash. That is just an abstraction to make it easier for people to understand.

What the correct hash actually uses is a target value. This target value is a 256 bit integer. In order for a block hash to be considered having a valid proof of work, it, when interpreted as a 256 bit integer must be less than or equal to the target value.

Since it is actually an integer comparison and not checking the number of 0 bits, there are far more possible target values.