<p>I use LINQ to Objects instructions on an ordered array. 
Which operations shouldn't I do to be sure the order of the array is not changed?</p>

Are you actually talking about SQL, or about arrays? To put it another way, are you using LINQ to SQL or LINQ to Objects?
The LINQ to Objects operators don't actually change their original data source - they build sequences which are effectively backed by the data source. The only operations which change the ordering are OrderBy/OrderByDescending/ThenBy/ThenByDescending - and even then, those are stable for equally ordered elements. Of course, many operations will filter out some elements, but the elements which are returned will be in the same order.
If you convert to a different data structure, e.g. with ToLookup or ToDictionary, I don't believe order is preserved at that point - but that's somewhat different anyway. (The order of values mapping to the same key is preserved for lookups though, I believe.)