Yes we understand such things from context:

Gittiğimiz eve = the house to which we are going (to is dropped)

Geldiğimiz ev = the house from which we are comning (from is dropped)

Yediğimiz restaurant = the restaurant at which we eat (at is dropped)

Ankara´ya gittiğimiz kız = the girl with whom we went to Ankara (with is dropped)

Denize atladığım adam = The man for whom I jumped into the sea (for is dropped)

Denize atladığım adam = The man with whom I jumped into the sea (with is dropped)

And if you want to be specific with above examples you may include kendi and taraf/iç/etc with postposition (English preposition)

Tarafına gittiğimiz ev = the house to which we are going

Tarafından geldiğimiz ev = the house from which we are comning

içinde yediğimiz restaurant = the restaurant at which we eat

Kendisi ile Ankara´ya gittiğimiz kız = the girl with whom we went to Ankara

Kendisi için denize atladığım adam = The man for whom I jumped into the sea

Kendisi ile denize atladığım adam = The man with whom I jumped into the sea

Thank you, tunci. si++, thank you.

I have noticed this disappearance of inlayed postpositions in texts many times but I guess I just needed someone to say it loud. Of course some occurances are clearer than others and there is just one probable interpretation that is likely to actualize in the listener´s mind. But then again in other cases (like this satın aldığı sentence) more alternatives tend to pop up, but this is of course a problem only in theoretical examples.

The participle tenses are still somewhat disorganized in my mind but there seems to be detailed info about this in the second link that you gave, si++. I´ll take it as a homework.

If we apply it to your examples:

         The men to whom the President spoke were patriots.

          We saw the man who my father bought the car from.

Başkanın kendilerine (kendileri ile) konuştuğu adamlar vatanserverlerdi.

Babamın kendisinden arabayı satın aldığı adamı gördük.

You are being so comprehensive, si++.

These examples, by the way, show that kendi is flexible enough to act as a hanger of grammatical elements without a special meaning of its own. When you don´t know where to put a troublesome suffix from your hands bring kendi to the scene.