You can use OAuth Rest API to authenticate Salesforce users. Refer thishttps://www.salesforce.com/us/developer/docs/api_rest/Content/quickstart_oauth.htm
If the issues are with the styles of templates, components then I would go with inspecting element with browser console else as said by @Fieke error.log will be the first place to check
You can write a simple service using JCR API to do that for you !You can refer this on using JCR APIhttps://helpx.adobe.com/experience-manager/using/programmatically-accessing-cq-content-using.html