[SalesForce] Salesforce integration with external system: Calling REST service API from Salesforce synchronously on record create and update event

Your future method will need some input to act upon, so a set of referral_advocate__c Ids (for bulkification purposes; this set of Ids would be built in the trigger on any record that has unique_ID__c != null ):

    set<Id> idSet = new Set<Id>{};
    for(referral_advocate__c r : trigger.new){
        if((r.unique_ID__c != null){
            idSet.add(r.Id);
            if(idSet.size()==100) {
                urlshortner(idset);
                idSet.clear();
            }
        }       
    }
    if (!idSet.isEmpty()){
       URLShortener(idSet);
    }

then also an update action: (forgive any typos / syntax errors, didn't get a chance to try it out in my dev org): Your future method will need some input to act upon, so a set of referall_advocate__c Ids (for bulkification purposes; this set of Ids would be built in the trigger on any record that has short_URL__C != null ), then also an update action:

@future(callout = true)
public static void URLshortner(Set<Id> idSet) {
    List<referral_advocate__c> rList = new List<referral_advocate__c>();
    Http http = new Http();
    for (referral_advocate__c r : [SELECT unique_ID__c FROM referral_advocate__c WHERE Id in :idSet]){
        HttpRequest req = new HttpRequest();
        req.setEndpoint('https://www.googleapis.com/urlshortener/v1/url?key=myapikey');
        req.setMethod('POST');
        req.setHeader('Content-Type','application/json');       
        req.setBody(JSON.serialize(
            new Map<String, String> { 'longUrl' => urls + r.unique_ID__c}));
        try {
            HttpResponse res = http.send(req);
            //parse your json response for the value

            r.short_URL__C = retValue;
            rList.add(r);
        } catch(System.CalloutException ce){
            // handle callout error
        }
    } 
    Database.SaveResult results = Database.update(rList, false);
    // handle DML error
}

try something like this to get you started out.

In Salesforce, everything is a CRUD operation. As far as your service is concerned, it needs to support CRUD OData operations. Your application would need to be modified to support CRUD operations. Databases typically support triggers, which is when some code is executed in response to a DML request. While salesforce does support using methods other than CRUD, you'll be left with the responsibility of writing your own Apex Code to support that logic.

If you wanted to translate standard CRUD operations into custom REST actions for OData, you could use the DataSource Connection class to implement custom Apex Code handlers, but this means you'll have to maintain your application and custom Apex Code. Simply rewriting your application to support proper CRUD operations would be more efficient than managing two sets of code just to have a common interface.

In your example, canceling a Booking should be as simple as calling POST /data/Booking('12345') with the post body { "@odata.type": "Booking", "Status": "Canceled" } (simplified for this example), with the result being that any business logic that needs to be executed (e.g. sending notifications, updating related records, etc) handled at the database level on the receiving end.