This method relies on some helper columns in your first spreadsheet, or in a separate sheet if you prefer.
MATCH() will return the row number a given value in an array.
INDEX() looks up this value in another specified array
So in row 1 of the the helper column (let's say column X), you want =MATCH(A1,SheetName!A:A,0)
This will return the row in the other sheet containing the ordernumber in A1.
Then in the next 2 columns, you want =INDEX(SheetName!C:C,$X1)
=INDEX(SheetName!D:D,$X1)
. This will return the count and the date from the other sheet in that row.
Then, in the last column you want =And(Y1=C1,Z1=D1)
. This will return TRUE if everything is the same.
Then use conditional formatting to make your highlights if you so wish.
This can all be condensed into a single formula and used as a conditional formatting condition on if you like, also, vlookup would work just as well here as index match. I've given you it all separated out as I think it's easier to follow what's going on and why it works, but I recommend you have a go at condensing it, as practice.
I hope this has helped.
Note, this won't work if the Order number is duplicated in the lookup list, as it only looks up the first occurrence in the table.