get row depending on the count of column and max value

I'll point out some of the problems first:

- There is a mistake in your sample data - 15-60-2015 is not a valid date

- In your attempt the syntax for MAX is incorrect - you've used a comma instead of a period. It should be

max(dbo.Replies.replyDate) as [lastreply]

- In your example SQL you have used column DocumentID but the table has docId

- Your expected results do not depend on UserId at all - they are the totals / max date per document type.

The key seems to be that you want to see all document types regardless of whether they appear in the Replies table. You can get those as follows

;WITH CTE AS
(
    select docid, count(replyid) as num, max(replyDate) as maxDate
    from Replies
    GROUP BY docid
)
SELECT docName, isnull(num,0), maxDate
FROM Documents D
LEFT OUTER JOIN CTE ON D.docid = CTE.docid

The query above gives your expected results as shown. Note there is no reference to userId

If, however, what you want is the details for a particular user then introduce UserId into the mix as follows

;WITH CTE AS
(
    select userid, docid, count(replyid) as num, max(replyDate) as maxDate
    from Replies
    GROUP BY docid, userid
)
SELECT docName, isnull(num,0), maxDate
FROM Documents D
LEFT OUTER JOIN CTE ON D.docid = CTE.docid
WHERE userid = 1 OR userid is null

Which gives results of

vacation    1   2015-06-14
private     0   NULL

Note the different date.

[EDIT - after OP request for further information]
To get the difference in dates in the format you've suggested is quite simple but can make the SQL look a little messy. I've pulled the messy bit into a 2nd common table expression to (hopefully) make it clear what is going on :

;WITH CTE AS
(
    select userid, docid, count(replyid) as num, max(replyDate) as maxDate
    from Replies
    GROUP BY docid, userid
),
CTE2 AS
(
	SELECT CTE.userid, docName, isnull(num,0) as numOfReplies, maxDate
	,DateDiff(dd, maxDate, getdate())      As days
		 , DateDiff(hh, maxDate, getdate()) % 24 As hours
		 , DateDiff(mi, maxDate, getdate()) % 60 As mins
	FROM Documents D
	LEFT OUTER JOIN CTE ON D.docid = CTE.docid
)
SELECT CTE2.docName, CTE2.numOfReplies,
Res = '(' + RTRIM((CASE WHEN CTE2.days > 0 THEN CAST(CTE2.days as varchar) + 'd ' END) 
	 + (CASE WHEN CTE2.hours > 0 THEN CAST(CTE2.hours as varchar) + 'h ' END)
	 + (CASE WHEN CTE2.mins > 0 THEN CAST(CTE2.mins as varchar) + 'm' END))
	+ ')'
from CTE2
WHERE userid = 1 OR userid is null

By way of explanation - use the DATEDIFF function to work out the number of days since MaxDate and Now. Use the same function modulo 24 to get the remaining number of (whole) hours over and above that number of days, and datediff modulo 60 to get the minutes over and above the number of days and hours. Be aware that time is ticking in that part of the sql - each call to getdate() will return a subtly different value, so don't go down to the millisecond level of comparison!

The final part of the query is just trying to get the output formatted. Under normal circumstances I would do that (i.e. output formatting) in my calling program e.g. probably something like

var res = new StringBuilder("(");
res.Append((days != 0) ? string.Format("{0}d ", days) : "");
res.Append((hours != 0) ? string.Format("{0}h ", hours) : "");
res.Append((mins != 0) ? string.Format("{0}d ", mins) : "");
res.Append(")");
Console.WriteLine(res.ToString().Replace(" )", ")"));