When should I place an adjective after the noun it modifies?
"I can beat you with my eye closed"
"I can spend the whole day undisturbed at the warehouse."
Those are not exactly adjectives. In English, almost always, and by "almost always" I mean 99.99% of the time, adjectives go before the noun they modify except in situations where adjectives like proper, extraordinaire and a couple more are used—those are termed postpositive or postnominal adjectives because they go after the noun. What you have up there though are what we usually refer to as past participles which in layman's terms are verbs that for all intents and purposes have become adjectives, but still strongly retain their verbal function—they still feel and sound exactly like verbs, even though formally they've now become words that describe qualities of objects, that is, adjectives.
I don't think there exist any hard and fast rules that can tell you precisely how to form and where and when use them. What I would recommend is when reading or listening to native speakers speak, try and take note of how they use them. It's really just a matter of being exposed to English long enough before you're able to form them on your own. In fact, they're so ubiquitous that you're going to see them used all the time. The following are a bunch of examples to get you started:
For me, a day without new knowledge is a day wasted.
The car, though completely broken, was still sold for pretty good money.
A past participle is the form of a verb used in forming perfect and passive tenses.