DateTime Extensions StartOfWeek, StartOfMonth and WorkingDays
First I'd like to pinpoint few details about methods' interface. You have an overloaded WorkingDays method, what I'd change:


Name does not explain what this functions does, I have to check its signature. Does it count the number of working days? Does it return a list of those days? For which period? Let's call it CountWorkingDaysInMonth() and there will be no need to guess.
Both freeDays and bankHolidays are not working days. There may be more: days company is closed, paid holidays and so on. Surely do not want to add a list for each one. Just take one changing signature to accept IEnumerable&lt;DateTime&gt; (and caller may easily use Enumerable.Concat() to build the right list.
Validate your inputs.


Inside the function I'd try to help the reader using the methods you already defined:

var beginningOfCurrentMonth = dt.StartOfMonth();
var beginningOfNextMonth = beginningOfCurrentMonth.AddMonths(1);


Note the explicative names and the fact that I'm reusing StartOfMonth() instead of duplicating its code (you'll see later why).

Let's introduce a generator (useful if you're working with consecutive dates):

IEnumerable&lt;DateTime&gt; AllDaysInInterval(DateTime start, DateTime end) 
{
    Debug.Assert(end &gt; start);

    for (var current = start; current &lt; end; current = current.AddDays(1))
        yield return current;
}


Declare a local function to determine if a day is a working day or not:

bool IsWorkingDay(DateTime day)
    =&gt; !freeDays.Contains(day.DayofWeek) &amp;&amp; !notWorkingDays.Contains(day);


Now you can count them:

return AllDaysInInterval(beginningOfCurrentMonth, beginningOfNextMonth)
    .Count(IsWorkingDay);


Short, easy to understand and you now created few reusable functions you may need elsewhere. Putting things all together:

public static int CountWorkingDaysInMonth(this DateTime dt,
    IEnumerable&lt;DayOfWeek&gt; freeDays,
    IEnumerable&lt;DateTime&gt; notWorkingDays)
{
    if (freeDays == null)
        throw new ArgumentNullException(freeDays);

    if (notWorkingDays == null)
        throw new ArgumentNullException(notWorkingDays);

    var beginningOfCurrentMonth = dt.StartOfMonth();
    var beginningOfNextMonth = beginningOfCurrentMonth.AddMonths(1);

    return AllDaysInInterval(beginningOfCurrentMonth, beginningOfNextMonth)
        .Count(IsWorkingDay);

    bool IsWorkingDay(DateTime day)
        =&gt; !freeDays.Contains(day.DayofWeek) &amp;&amp; !notWorkingDays.Contains(day);
}




Now it's time to go back to StartOfMonth(). Is it always 1st the first day of the month? No. Not every date is a valid date in every calendar. You may, or may not, need to care about this but you should clearly document it (and be aware of).



In StartOfWeek() you can make your code easier to read. 


int diff = ((dt.DayOfWeek - startOfWeek)) % 7; has unnecessary parenthesis and diff does not say anything about its content. Also it's not used if startOfWeek is Sunday.
-1 * diff should simply be -diff.
IMO (7+(startOfWeek - dt.DayOfWeek)) % 7 is clearer if moved outside, to a local variable.


What to do? Just (temporary!) introduce a local function to calculate the number of days from the beginning of the week:

int NumberOfDaysFromBeginningOfWeek()
{
    if (startOfWeek == DayOfWeek.Sunday)
        return (7 + (startOfWeek - dt.DayOfWeek)) % 7;

    return (dt.DayOfWeek - startOfWeek) % 7;
}


Is it what we want? Doesn't it look too complicate? It does then it's probably wrong. Algorithm must be much simpler than that. Let's first calculate the number of days elapsed from the beginning of the week without any special case:

int daysFromBeginningOfWeek = dt.DayOfWeek - startOfWeek;


What's wrong with that? Well, we're relying with enumeration values but week may begin any day (it depends on the culture). What may happen if our day is before the beginning of the week? Number goes negative. Let's add the number of days in a week and it will be right:

int NumberOfDaysFromBeginningOfWeek()
{
    int count = dt.DayOfWeek - startOfWeek;
    if (count &lt; 0)
        return count + 7;

    return count;
}


Note that I'm simplifying this code with a huge assumption: there are always seven days in a week. It's not true and you should read the value from the calendar. Final code will be slightly more complicate than this but I guess you've got the idea. Putting things together:

public static DateTime StartOfWeek(this DateTime dt, DayOfWeek startOfWeek)
{
    return dt.AddDays(-NumberOfDaysFromBeginningOfWeek());

    int NumberOfDaysFromBeginningOfWeek()
    {
        int count = dt.DayOfWeek - startOfWeek;
        if (count &lt; 0)
            return count + 7;

        return count;
    }
}


In this last case local function is more educational than useful, reader should absolutely feel free (!) to replace it with a local variable (with a proper descriptive name.)

Please note: I wrote all this code here without any testing. Do not underestimate date/time handling and write your own huge, big, extensive unit testing to include all corner cases, calendars and cultures you may think of and, most importantly, never ever make any assumption about dates. If there is a property somewhere (Calendar, Culture or DateTime) then use it.