[SalesForce] Salesforce API – An existing connection was forcibly closed by the remote host

Client Key - its a long code string

This is what you do when you create a connected app. Go to Setup > Create > Apps, and create a new Connected App. Once configured, it will generate the Client Key that your contractor will need to connect their app to your org.

Authorization URL - This normally looks similar to: https://test.salesforce.com/services/oauth2/token

Unless you're using My Domain, that's exactly what it will look like. Even if you are using My Domain, using that should still allow connection to your sandbox, as it's a universal login endpoint.

DSR Endpoint(s) - This is where I will push the briefing data to. This normally looks similar to this, but please give me the full URL: /services/data/v29.0/sobjects/Conference__c/<>

Nobody can give you the "full" URL, because we don't know where you're located (e.g. which pod, or if you're using My Domain). The developer will need to use the instance_url parameter that they receive when using the token exchange.

For example, if you are on cs1, it would be: https://cs1.salesforce.com/services/data/v29.0/sobjects/Conference__c/ in order to access the Conference__c object's describe data in your sandbox.

You have your password + token in the wrong order. Use it as the following (without blank spaces and <>.):

<password><token>