Find start and end date by week number , start day of week and year

The first issue you have is to define "week number". I'm going to assume you mean the ISO Week Number (ISO week date - Wikipedia[^]) which equates to CalendarWeekRule.FirstFourDayWeek. To see why this is important consider this code snippet, which lists the week that 2017-January-16 falls in, in the Gregorian calendar, for the 3 different options for counting weeks:

var cc = new GregorianCalendar();
dt = new DateTime(2017,1,16);
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Monday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Monday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Monday));
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Tuesday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Tuesday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Tuesday));
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Wednesday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Wednesday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Wednesday));
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Thursday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Thursday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Thursday));
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Friday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Friday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Friday));
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Saturday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Saturday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Saturday));
Console.WriteLine("Week {0} {1} {2}", cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Sunday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFullWeek, DayOfWeek.Sunday), cc.GetWeekOfYear(dt, CalendarWeekRule.FirstDay, DayOfWeek.Sunday));

It gives the results

Week 3 3 4
Week 2 2 3
Week 2 2 3
Week 3 2 3
Week 3 2 3
Week 3 2 3
Week 3 3 3

Your next problem is your enum. Firstly it is not well formed, MS advise that enums should always have an entry with a value of 0. I really can't see why you don't just use the standard enum - after all you don't really care about the number, just the "name" of the day

[Serializable]
[ComVisible(true)]
public enum DayOfWeek
{
    Sunday = 0,
    Monday = 1,
    Tuesday = 2,
    Wednesday = 3,
    Thursday = 4,
    Friday = 5,
    Saturday = 6,
}

To use the standard DateTime functions you are going to have to convert your enum to the standard, which you can do like this:

var Week_start = EN50160DayOfWeek.Tuesday;
var realday = (int)Enum.Parse(typeof(DayOfWeek), Week_start.ToString());

The next step is to work out a date for the week number you require, based on your configurable start of week day. In the code below I've chosen a "brute-force" approach - start on the first day of the year and keep adding a day until you get to the week you want. That is obviously going to be the first day of that week and adding 6 days will give you the date of the last day in that week:

var year = 2017;
var week_number = 3;
var Week_start = EN50160DayOfWeek.Tuesday;

var realday = Enum.Parse(typeof(DayOfWeek), Week_start.ToString());

var cc = new GregorianCalendar();
var dt = new DateTime(year, 1, 1);
for (var i = 0; i < 365; i++)
{
    dt = dt.AddDays(1);
    if (week_number == cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, (DayOfWeek)realday)) break;
}

var startOfWeek = dt;
var endOfWeek = startOfWeek.AddDays(6);

If you think that method is too inefficient for weeks later in the year, then you can increment the date of YYYY-Jan-01 by 1 until you get to the start of Week 1. This isn't as silly as it sounds as it is only CalendarWeekRule.FirstDay that will guarantee Week 1 starts on 1st January. Once you have the start date of week 1 just add the appropriate number of days to find the week you want. Like this:

var year = 2017;
var week_number = 3;
var Week_start = EN50160DayOfWeek.Tuesday;

var realday = Enum.Parse(typeof(DayOfWeek), Week_start.ToString());

var cc = new GregorianCalendar();
var dt = new DateTime(year, 1, 1);
while (cc.GetWeekOfYear(dt, CalendarWeekRule.FirstFourDayWeek, (DayOfWeek)realday) > 1)
{
    // Handle start of January being week 52 or 53 of the previous year (2017 for example)
    dt = dt.AddDays(1);
}
var startOfWeek = dt.AddDays((7 * (week_number - 1)));
var endOfWeek = startOfWeek.AddDays(6);