How can we get Customers info and Opportunities info in c# using salesforce api . or is there any API exist that can be used to get customers/contact info and opportunities info from salesforce API
You can use Salesforce standard Rest API to access the opportunities or any other object.
Try Workbench: It's an awesome tool where you can build rest-urls to access different type of data.
These are some REST-URLs to access different type of records from Salesforce.