Implemention of ISO 17025

You asked

How we merge the two system in records and procedures and we have to point it out  in the quality manual , or every system ISO 9001 and ISO 17025  should be separate in their  records and procedures.

This will depend on your organisational structure and whether ISO 9001 applies to just the laboratory, or to other departments in the organisation. If the same person is responsible for both systems and you wish to integrate them then, just add the required document and record you need for ISO 17025. I then recommend rewriting the Quality Manual to have one manual to cover both ISO 17025 and 9001 systems.  If there are different people responsible for each then keep the manuals separate and in the ISO 17025 quality Manual refer to the ISO 9001 manual for overlapping approaches such as handling complaints, procurement, and certain personnel requirements (e.g recruitment). Have a look at a previous question and answer for more information at https://community.advisera.com/topic/design-development and https://community.advisera.com/topic/are-there-any-things-in-iso-9001-not-covered-by-iso-17025

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The second question :  we want to participate in PT ,Profechency Test  in food analysis ,cosmetic ,detergents , paints ,lubricants oil  , textile, leathers, paper , construcure analysis field , could you recommend  some of PT service  providers.

This is a very broad scope. I suggest you speak to your selected or an accreditation body in your region. You can also search for accredited u Proficiency Scheme providers on the accreditation body websites .
You should also have a look at the Proficiency Testing (PT) scheme database, EPTIS. at https://www.eptis.org/about.htm. This should be helpful.

You also asked

could I see a simplified way to write a plan to implement the international standard ISO 17025

Have a look at the Project Plan for ISO/IEC 17025 implementation as well as the very useful Project checklist for ISO 17025 implementation. They are available to download for free at https://info.advisera.com/17025academy/free-download/project-plan-for-iso-17025-implementation and https://info.advisera.com/17025academy/free-download/project-checklist-for-iso-17025-implementation.

Lastly, you asked

If a new employee occupies a quality manager, should it be within his plan to make sure that the work in the laboratory is done correctly and to follow up to what extent the previous quality manager applied the requirements of ISO 17025 to know what has been achieved and what needs to be completed, or works directly on preparation for proficiency tests According to the administration's request, and this is specified in his plan.

This will depend on your organisational structure and the job profile. For example, what other positions are there in the laboratory ? Typically a laboratory or technical manager is responsible for day to day operations and quality control and the quality manager (or a number of designated people) performs the role of ensuring the overall QMS is functional. This involves, as example, Internal Audit management, arranging or overseeing the proficiency testing schemes and the Management review process.