I would recommend implementing Batch Apex

You need 2 classes. Copy and paste this code into a class you are going to name as UpdateEmailAlertDate and modify the query  in my class for c.SecCon_Checkbox__c = true to change it to the field name extraction_type__c='Manual' or whatever the field value you have.

#1) UpdateEmailAlertDate - This class goes through and sets the updates the Email_Alert_Date__c to Today() based on whether you are precisely 14, 7, 3, 1, 0 days away from your Extraction_Date__c

global class UpdateEmailAlertDate implements Database.Batchable<SObject> {

    global Database.QueryLocator start(Database.BatchableContext BC){

        String query = 'Select c.Name, c.Id From Contact c '
        + 'where c.SecCon_Checkbox__c = true and ( c.Extraction_Date__c = NEXT_N_DAYS: 14 or '
        + 'c.Extraction_Date__c = NEXT_N_DAYS: 7 or c.Extraction_Date__c = NEXT_N_DAYS: 3 or '
        + 'c.Extraction_Date__c = NEXT_N_DAYS: 1 or c.Extraction_Date__c = TODAY)';
    return Database.getQuerylocator(query);
    }
    global void execute(Database.BatchableContext BC, List<sObject> scope){
        List<Contact> contactList = new List<Contact>();
        system.debug('contact size '+scope.size());
        for(sObject s : scope){
            Contact o = (Contact)s;
            system.debug('contact name '+o.Name);
            o.Email_Alert_Date__c = System.today();
            contactList.add(o);
        }
        update contactList;
    }

    global void finish(Database.BatchableContext BC){
        // Get the ID of the AsyncApexJob representing this batch job
        // from Database.BatchableContext.
        //Query the AsyncApexJob object to retrieve the current job's information.
        AsyncApexJob a = [SELECT Id, Status, NumberOfErrors, JobItemsProcessed,
        TotalJobItems, CreatedBy.Email FROM AsyncApexJob WHERE Id = :BC.getJobId()];
        // Send an email to the Apex job's submitter notifying of job completion.
        Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
        String[] toAddresses = new String[] {a.CreatedBy.Email};
        mail.setToAddresses(toAddresses);
        mail.setSubject('Apex Sharing Recalculation ' + a.Status);
        mail.setPlainTextBody
        ('The batch Apex job processed ' + a.TotalJobItems +
        ' batches with '+ a.NumberOfErrors + ' failures.');
        Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail }); 
    }
}

#2) ContactUpdateScheduler - Copy the code as is no change necessary on this class

global class ContactUpdateScheduler implements Schedulable {
    global void execute(SchedulableContext sc){
        database.executeBatch(new UpdateEmailAlertDate());
    }
}

#3) Go into Your Name - Setup - Develop - Apex Classes - Schedule Apex

Give a Job name and select the ContactUpdateScheduler to run.

Tip: If you want to run it once, just use Start Date and End Date as the same and choose a time, else run it as frequently as you want.

You can monitor the job using Monitoring Scheduled Jobs and Apex Job