Ajax function with a callback
From a short review;


patient is a global variable, global variables are bad
var patient = [] is more idiomatic than var patient = new Array();
Comments should be all German or all English (I would go for all English, its the common language of the developers)
You can group switch labels, this is valid JavaScript:

        switch(key){
            case "id":
            case "kundennr":
            case "termart":
            case "userId":
                res[i][key] = parseInt(value);
                break;
            case "client":
            case "title":
            case "description":
                res[i][key] = value;
                break;
            case "start":
            case "end":
                res[i][key] = new Date(value);
                break;
            default:
                console.log("unbekannter Datentyp " + key);

Your data fields should be either all English or all German (you have userId, but also kundennr), here as well I would go for all English
Since value already contains res[i][key] for "client", "title", etc., you should probably comment on that 
Since this is real, you should not log to console for an unknown data type, you should call a REST service that will log this entry in a database table, and even possibly send out an email to developers 
var key in Object.keys(res[i]) is safer than var key in res[i], you never know when someone decides to extend Object
Your indenting is off, consider using a beautifier