[SalesForce] how to retrieve specific fields for Object using REST api

You can generate a WSDL file for your org by going to Setup->Build->Develop->API and click on 'Generate Enterprise WSDL'. The Enterprise WSDL will contain your full schema in xsd structure.

For the REST API, you don't need to use the WSDL. You can explore the API by going to https://{instance}.salesforce.com/services/data/v24.0

For an interactive explorer, check out apigee's salesforce console: https://apigee.com/console/salesforce

Fetching the WSDL/XSD schema from the REST API is not possible by my knowledge.

I hope the below answers will help you to create a better solution:

1. What is the maximum number of records that can be sent as Response (JSON) ?...What is the suggested limit ?

   Answer:
   CPU limit ,Heap size limit etc all will generally apply as same applied in normal apex class.
   Records: 50,000 records in a rest api context
   DML Statements: 150 DML
   SOQL Statements: 100 SOQL limit of context
   Response Size : 3 MB
   API Requests: Each request sent to rest apex class will count against number of API calls to your org & number of API calls allowed for your org depends on edition and as well as licenses.
   

2. In a scenario where we send like 100 records to them and if they fail to receive it...what will happen and how we (Salesforce team) will know ?

   Answer: If rest service is not able to receive the request or failed, it will return the response with error message and status code.

3. What if they query for like 100000 records and how we can split the result set into batches and send it to them ?

   Answer: I think there is no way to do this in rest API. as it returns only 50,000 records in transition. I think instead of using apex rest-api, use standard rest api to perform a query which can result in batches but for that you have to give access to your folks.

Note: As you have mentioned folks have no access or license in Salesforce, then you have to expose the rest apex class publically which can be a security breach!!