[verb た-form] + [noun] [verb て-form] + いる + [noun]
A verb describes a noun by standing straight in front of it, where English uses a relative clause after it: "the book that I bought". There is no word for "that" or "who". In the た-form the action is done; in the ている form it is going on, or its result still holds.
Nothing goes between the verb and the noun – no の, no な.
The clause can carry its own subject, object and time words, all in front of the noun, and the noun can then play any part in the main sentence.
The subject of the describing clause takes が, or の, never は. は would make it the topic of the whole sentence.
ている describes an action in progress, or a state that resulted from an action and still holds. With すむ住む, けっこん結婚する or かける (glasses), it is a state, not something happening right now.
The た-form says the action is done by the time of the main verb, not necessarily before now. It also turns some verbs into plain descriptions: こわれた壊れたかさ傘, "a broken umbrella".