Is this correct way to use cookies from a syntax point of view?
At the expense of having a little more code, I would use a localStorage polyfill [2].

With that code in place you no longer need to keep the create and read cookie methods. You also don't need the code wrapping get_data and set_data. Your resulting code would look something like this:

set_last_page = function(cluster) {
    if (!localStorage.getItem("Page")) {
        if (!localStorage.setItem("Page", JSON.stringify(cluster))) {
            log("Current Page: Stored");
        } else {
            log("Current Page: Store Failed");
        }
    } else {
        localStorage.removeItem("Page");
        if (!localStorage.setItem("Page", JSON.stringify(cluster))) {
            log("Current Page: Stored");
        } else {
            log("Current Page: Store Failed");
        }
    }
}

get_current_page = function() {
    if (localStorage.getItem("Page")) {
        var last_page = JSON.parse(localStorage.getItem("Page"))
        log("Last Page: " + last_page);
        return last_page;
    } else {
        log("Last Page: Inexistent");
        return 1;
    }
}


From here I would make a few changes:


You don't need to check for existence or remove an item from storage to change it. 
The logging code is unnecessary.
Using JSON.stringify and JSON.parse is considerable overkill for converting between a string and a number.


Taking care of these would leave me with this code:

set_last_page = function(cluster) {
    localStorage.setItem("Page", cluster+'');
}

get_current_page = function() {
    return +(localStorage.getItem("Page") || 1); 
    //localStorage.getItem("Page") will return either 
    // a number &gt;= 1 (as a string), undefined or null 
    //so '|| 1' will take care of the latter cases
}


Finally, I dislike the fact you are initializing these variables as function expressions (statements) and don't end them with semicolons (either add the semis or make them function declarations). I would also rename things to be more consistent and in line with my preferred naming conventions for javascript:

function setPage(page) {
    localStorage.setItem('page', page+'');
}

function getPage() {
    return +(localStorage.getItem('page') || 1); 
}