Do you think that the job of a Warehouse Manager should mostly be associated with distribution?

They are often run seperately, however, as they compliment the bigger role they it works so much better having a Warehouse and Transport mnanager combined

yes, managing the inventory is the part of distribution system in supply chain management. 

they are relative to each other , but they could be separated no problem it won't ruin the business , but in my opinion if they are associated it will add value

Yes! ofcourse

It’s not must, depend of your operations "is it big or small" if it's big then you need to separate if it's small no need to separate.
In my view If each one of them have a manager then more focus and fast improvements will happen in both areas but more conflict will happen on ground.
If both divisions have the same manager, Improvements will happen in both areas depend of the manager capabilities and smooth operations will happen.

Yes, they complete each other

Warehouse are divided into two parts: the first is serving the production and maintenance operations, or what you can call the internal operations, which are: raw materials warehouse, spare parts warehouse, tools and devices warehouse.
Normally, the warehouse in this type of stores does not need to be qualified in distributing activities.
The other type of warehouse contains the finished products like: plastic house holds products, medicines, cloths, toys, electric house appliances.
The warehouses that contains the same are normally running two tasks: the first is the normal warehouse operations: holding warehouse registry (in - out transactions), receiving the goods, organizing them one the shelves and keeping them safe, and the second task is managing customers orders according to sales department policies, procedures and instructions.
In this type of warehouses: the warehouse manager, and the store keeper who assists him and all other staff, should be qualified and well trained to deal with an additional task "customers relations" .
So they should keep an eye on the stocks records and compare them with the planned sales, drawing the attention of sales persons to the situation of current stock on hand, and alerting them about the dead stocks that should be sold.
These relations, with the sales persons and customers, are not found in the first type of warehouses mentioned above , and should be possessed by the warehouse manager who manage such warehouses.

no 

not necessary ,,,

Distribution forms an important part in the Warehousing process.