The clause in the underlined part of sentence 3 is a(n) clause.

dependent (because it can not stand by its self)

A dependent and essential adjective clause.

Explanation:

A dependent clause is a clause that does not express a complete thought on its own, and therefore it cannot stand by itself, it needs to depend on another clause to have sense. In a sentence, this type of clause may function as an adjective, adverb or noun.

In the sentence: Wherever there are animal droppings, there is a constants rain of organic matter that feeds the bottom dwellers, the last clause works as an adjective because it describes the noun "organic matter". And, at the same time, this adjective clause is essential because it is not set off by commas and its information is necessary to fully understand the sentence.

buy a huge library full of all the books ever written

the animal shelter ad with animals in cages, starving and dying.

explanation: