First of all,
S + V + O + Adj + to Inf + O
is not a single construction. It is a string that can be the result of a large number of possible derivations.
Second, everything in such constructions depends crucially on what that V is. Not all predicates take infinitive complements, and of those that do, some allow for to mark the infinitive subject, and some don't; some have indirect object and others don't; some allow to to mark the infinitive verb, and others don't, etc.
There are a lot of variations, all depending on the matrix predicate. To see just how many, see here.
As to the two sentences provided,
Windows makes it easier for you to install the program.
comes from something like
- Windows makes [for it to be easier [for you to install the program]]
i.e, there are three clauses here: one has make as its predicate, one has be easier, and the third has install. The middle clause has undergone Extraposition, which produces the dummy it, from
- ... [for you to install the program] be easier
Notice that make takes an infinitive without to (make it work but not *make it to work), and auxiliary be is deleted before stative predicate adjectives (make it tasty but not *make it be tasty). Details, details.
Easy/easier, the predicate of the second clause, takes an infinitive subject complement; if the subject of the infinitive is specified, it must take for.
The second sentence
You may find it difficult to locate the bug
also has three clauses, and again the second one has a predicate adjective infinitive (to be difficult) with to deleted because it's a complement of find. That clause has also undergone Extraposition from
- ...[(for you) to locate the bug] be difficult
However, unlike the first sentence, the dummy it from extraposition has been B-Raised from being the subject of (be) difficult, to become the direct object of find. The last clause has lost its subject (for you) by Equi from the subject of find.
This is the kind of problem one encounters when treating grammar as composed of strings of words or word types. Grammar is constructions, not strings, and constructions are almost always governed by predicates. Without knowing the clause and predicates, it's impossible to talk about grammar usefully.
Taking your example: "[This is the] man who the authorities refused to admit existed," you have correctly identified that you want to look at the variation "The authorities refused to admit he existed." In that variation "he" is a subject of a clause. "Whom" is used for as a pronoun for the object of the dependent clause, not when the clause itself is the object of the independent clause. So, while "he existed" is the object of the variation, "he" is the subject, and that's what matters.
To take another example:
This is the man whom the doctors refused to admit.
is correct because "the man" is the object of "to admit." In your example, they were not refusing to admit the man, the were refusing to admit a statement about the man.
Best Answer
There are sentences that start with "for verbing" but that one isn't a particularly good one:
So if your question is "can I do this?" the answer is yes. If your question is something else ("What is this called?" "Is there generally a better way to word these sentences?" "Is my particular example grammatical?") then I suggest you edit the question to include an actual question.