There are a few things to mention regarding the grammar of construct chains. First, you will notice the dash-like line between some of the words in the examples above. This is called a maqqef and functions much like a hyphen in English. However, it has more to do with accents than anything else. It will sometimes appear in a construct chain and other times will not. Either way, the meaning of the construct chain is unaffected.
Secondly, pronoun suffixes are actually a form of construct chain. There is an example of this above, where a more wooden translation would have been, “the house of the brothers of the lord of me.” As you can see from this translation, the pronoun suffix is actually just another link in the chain. The only way it is different than other words in a construct chain is the fact that it is a suffix.
Finally, it is important to understand definiteness with regards to construct chains—whether the construct chain contains the sense of the definite article (i.e. ה in Hebrew, “the” in English). An entire construct chain in Hebrew is understood to be definite if the final word in the chain is definite—either because it is a proper noun, a pronoun suffix or possesses the definite article. From the examples above, you can see that they are all definite, except for the last example. The first three are definite because they end with a proper noun. The fourth is definite because the 1cs pronoun suffix (“my”) at the end of the chain. The fifth example is definite because of the presence of the definite article. But the last example is indefinite and hence is translated, “a tree of life.”