Beginning with your third example, the sentence structure has the
SVO stands for Subject + Verb + Object. This is a very common sentence structure in English.
Subject = "I"
Verb = "saw"
object = "him"
In this case, the participle
running modifies the object,
him. It would be possible to modify the object further with prepositional phrases, or the participle could be modified with adverbs.
Example  modified with a prepositional phrase:
I saw him running down the street.
Example  modified with a prepositional phrase and an adverb:
I saw him hurriedly running down the street.
The adverb could be placed at the end of the preposition depending on what you wanted to emphasize. Such as:
I saw him running, down the street, hurriedly.
The type of verb modifying the main subject would not effect the object's participle.
For example, the following sentences are all also correct:
I see him running.
I will see him running.
I did see him running.
I intend to see him running.
The first two examples in the query seem more ambiguous in their meaning, and border on nonsensical. They would be better understood in context, and colloquially they would not necessarily be considered incorrect. Again, the example sentences have the
SVO construction. Normally, in English, the adjectives come before the nouns.
Alternatively, a more standard way would be as follows:
I bought a good looking pen.
I bought a good pen.
I bought an attractive pen.
In the first example given, perhaps if the "looking good" modified the subject this would make more sense, but it would, in this case, be written like this:
I, bought a pen, looking good.
The commas more clearly show that "looking good" modifies the subject, "I".
or the construction could be altered for more clarity as follows.
I, looking good, bought a pen.
In the second example, without the commons. The presumed longer form, "I bought a pen that was looking good." is more correct.