Testing future callout method

Question

I am attempting to test a @future callout class that pings another class to make an API call and update some fields in the Lead object. I am using the mock http method and here's the script:

@isTest
private class MMarkAPITest
{
    @isTest
    static void MMarkAPIUnitTest() {

        //create a lead with website address of testapp.com
        Lead l = new Lead
        (company = 'Test Company',
        status = 'Open',
        website = 'testapp.com',
        firstname = 'Guy',
        lastname = 'Test');
        insert l;

        Test.startTest();
        //set-up a mock callout
        Test.setMock(HttpCalloutMock.class, new MMarkAPITestHttpCalloutMock());
        // Call method to test.
        // This causes a fake response to be sent
        // from the class that implements HttpCalloutMock.

        MMarkAPI.MMarkAPIFutureCallUpdater('testapp.com');

        Test.stopTest();
        //access the lead entity
        Lead updatedLead = [select Name, Country, Description from Lead where Id = :l.Id];

        System.debug('lead is ' +updatedLead);

        System.assertEquals(l.description, 'description');
        System.assertEquals(l.MZ_Lo__c, 'country');
        System.assertEquals(l.YY_Totag__c, 'total funding');

    }
}

However when running it with System.assertEquals it fails (all assertions return null value).

On the other hand, when I remove the System.assertEquals the test succeeds but also returns the following message:

System.CalloutException: You have uncommitted work pending. Please commit or rollback before calling out

I came across some information regarding DML queries and testing callouts (e g here), but I am struggling to apply it to this problem.

Adding the FutureCallUpdater:

/** CALL FOR THE INSERT UPDATE TRIGGER  **/
@future(callout=true)
public static void MMAPIFutureCallUpdater(string domain){
    MMAPIUpdater(domain);
}

This triggers that:

public static void MMAPIUpdater(string domain){
    list<Lead> leads = [SELECT MM_Description__c FROM Lead WHERE Website LIKE :domain limit 1];

    HttpResponse res = MMAPIcallout(domain);

    if(res.getStatusCode() == 200 && string.isNotBlank(res.getBody())){

      string body = res.getBody();
      //system.debug('body before replaced is'+body);
      body = body.replace('"currency":', '"deal_currency":');
      //system.debug('body after replaced is'+body);

      JSON2Apex companyProfile = MMAPIParse(body);
      system.debug('company profile is' +companyProfile);

      //single ocurring variables
      string description = companyProfile.data.description;
      //system.debug('description is'+description);
      string country = companyProfile.data.country;
      //system.debug('location is'+country);
      string employees_current = companyProfile.data.employees;
      //system.debug('employees_current is'+employees_current);
      string employees_month_ago = companyProfile.data.employees_month_ago;
      //system.debug('employees_month_ago is'+employees_month_ago);
      string employees_6_months_ago = companyProfile.data.employees_6_months_ago;
      //system.debug('employees_6_months_ago'+employees_6_months_ago);
      string total_funding = companyProfile.data.total_funding;
      //system.debug('total_funding is'+total_funding);
      string last_funding_amount = companyProfile.data.last_funding_amount;
      //system.debug('last_funding_amount is'+last_funding_amount);
      string last_funding_date = companyProfile.data.last_funding_date;
      //system.debug('last_funding_date is'+last_funding_date);

      //convert list variables into strings

      //business_models
      List <String> businessModels = companyProfile.data.business_models;
      string commaSeparatedBusinessModels = '';
      if(businessModels != null){
        //system.debug('the business models list it' +business_models);
        for (String model:businessModels ){
          commaSeparatedBusinessModels += model + ', ';
        }
        //system.debug('comma separted business models are'+commaSeparatedBusinessModels);
      }

      //acquired_by
      List <Meta> acquiredBy = companyProfile.data.acquired_by;
      string commaSeparatedAcquiredBy = '';
      if(acquiredBy != null){
        for (Meta acquirer:acquiredBy){
          commaSeparatedAcquiredBy += acquirer + ', ';
        }
      }

      // singular variables to be inserted into Lead objects
      for(Lead l:leads){
        l.MM_Business_Models__c = commaSeparatedBusinessModels;
        l.MM_Description__c = description;
        l.MM_Location__c = country;
        l.MM_employees_current__c = employees_current;
        l.MM_employees_1M_Ago__c = employees_month_ago;
        l.MM_employees_6M_Ago__c = employees_6_months_ago;
        l.MM_Total_Funding__c = total_funding;
        l.MM_Last_Funding_Amount__c = last_funding_amount;
        l.MM_Last_Funding_Date__c = last_funding_date;
        l.MM_Acquirers__c = commaSeparatedAcquiredBy;
      }

      try {
        update leads;
      }   catch (DmlException e) {
        System.debug(e.getMessage());
      }

      //lists of variables to be inserted into custom objects

      /*


      MM_Funding_History__c

      To ensure deals are added only once (no duplicates), the script invokes the lead with the relevant ID number
      (obtained by looking for a lead with the relevant domain) and creates a string of funding deal dates (dealDatesInString)
      separated by a comma. Subsequently, upon lead update only funding rounds with the date
      not appearing on the list are added to the Lead (if (!dealDatesInString.contains(deal.funding_date))

      */

      string LeadId = getLeadID(domain);
      List <Funding> funding = companyProfile.data.funding;
      List<MM_Funding_History__c> dealsList = [SELECT MM_Date__c FROM MM_Funding_History__c WHERE MM_Funding_History_To_Lead__c = :LeadId];
      //system.debug('the list is' +dealsList);

      //ensuring that the deals are added only once
      string dealDatesInString = '';
      for (MM_Funding_History__c d :dealsList){
        dealDatesInString += d + ', ';
      }
      //system.debug('deal dates string is' +dealDatesInString);

      for(Funding deal:funding){
        //ensuring deals are added only if they're not already on the list (using MM_Date__c as unique identifier)
        if (!dealDatesInString.contains(deal.funding_date)){
          MM_Funding_History__c row = new MM_Funding_History__c(
          MM_Funding_History_To_Lead__c = getLeadID(domain),
          MM_Amount__c = deal.amount,
          MM_Date__c = deal.funding_date,
          MM_Funding_Type__c = deal.series,
          MM_Investors__c = deal.investors,
          MM_Currency__c = deal.deal_currency);
          //system.debug('this is row' +row);
          insert row;
        }
      }

    }
  }