The customer might not be following you, hence the direct messages are not getting delivered to the customer.

Survey links are not visible on Sprinklr. You will see a blank space in the place of link. Survey links will only be visible to your customers to whom the survey was sent.

Make sure you are using the right placeholder for survey link i.e., %%[SURVEY_LINK].

If a question has multiple options viz. Option 1, Option 2 and Option 3 with the reporting statistics as
Option 1 - 23
Option 2 - 34
Option 3 - 45

And if you later change the options as Option One, Option Two and Option Three, then reporting statistics will be as follows
Option 1 - 23
Option 2 - 34
Option 3 - 45
Option One - 20
Option Two - 15
Option Three - 30

(where 20, 15 and 30 users have selected Option One, Option Two and Option Three, respectively after the change)

To view a unified reporting after making any changes in the options, create a custom metric for each option.
Choice 1 = Option 1 + Option One
Choice 2 = Option 2 + Option Two
Choice 3 = Option 3 + Option Three

where Choice 1, Choice 2 and Choice 3 are custom metrics.

Yes, you can customize the survey link in Rule Engine through a URL Shortener which can be added in Platform Settings. Create a Case Update rule and under Actions to "Survey", select URL Shortener as a Condition and select the desired URL shortener from the corresponding dropdown to create a Vanity URL.

Yes, the answers to survey questions can be mapped at the case level in Reporting by selecting Social Analytics as a Data Source.

While plotting it on a widget, select Survey Answer Count as a metric. Under Filters, you can select the language for which you want to view the answers.

Yes, after creating the widget in Reporting, you can take the export of the survey answers. Hover over the Options icon  in the top right corner of the widget. Next, hover over the Export Widget option and select the desired option.