Is it possible to use Square without payment processing? If we use local payment processing provider with Square POS?

Yes, you can use Square without the Card processing.  you will have to enter the sale as other payment and maybe enter a reference number from the other CC terminal.

Thank you @VanKalkerFarms 
How can I contact the Sales for further information? Can I contact them via email?

Can you please guide me on how to contact sales team ??

You wouldn't need to contact the sales team to use Square to record payments, @alihusain2021 🙂 Download the Square Point of Sale app, and check out this guide to get started.