All Manufacturing organizations must have costing department. Do you agree?

I strongly agree.

Cost Accounting is a process of collecting, recording, classifying, analyzing, summarizing, allocating and evaluating various alternative courses of action & control of costs. Its goal is to advise the management on the most appropriate course of action based on the cost efficiency and capability. Cost accounting provides the detailed cost information that management needs to control current operations and plan for the futureSince managers are making decisions only for their own organization, there is no need for the information to be comparable to similar information from other organizations. Instead, information must be relevant for a particular environment. Cost accounting information is commonly used in Financial accounting information, but its primary function is for use by managers to facilitate making decisions.

YES BECAUSE WITHOUT THIS DEPARTMENT WE CANNOT CONTROL THE MANUFACTURING COST.

Yes All manufacturing organizations must have costing department

its depend on the scale of business and product type, production manager should be aware of coasting and management accountant and he could manage the cost of goods for the small size or typical production(even in large scale), costing department needed for big complex organization.

budget and cost is tow different things.  

It is important for manufacturing organizations since they have to have estimates of budgets and also keep in check of the manufacturing costs.

Yes.

The reason being ,a Job order costing system delivers a very efficient method to calculate the exact expenses required for materials, labor, and overhead before producing an item. Getting relevant information about manufacturing costs allows you to evaluate profitability and decide whether you should produce that particular item or not.

If they are using Lean Manufacturing may it doesn't required a separate department as each department has to follow his cost & involved in the year budget, but all these departments cost will controlled by F&A department. 

The cost accounting it's very necessary in all manufacturing organizations, but in the small scale organizations no need for department with more than one employee, only one person can do this job. 

any company needs budgets , to measure progress and profits 

It is important as budget estimation