I understand that that the correct spelling of the legal term for law of residence is: "jus domiciliī" (with a line over the i), and "just solī" (with the line) for law of soil. Would it also be jus nexī (with the line) for law of connection?
The "line" to which you are referring must be a macron, a vertical line that is used over vowels long by quantity, commonly called "long marks." These are used only as a tool for learning Latin and are dispensed with after that point. You will also see the long vowels so marked in dictionaries, as they can affect the meter of Latin poetry.
However, in actual texts of Latin authors, as well as Latin phrases used in English texts, vowel are not so marked. The term "jus nexi" is a modern legal Latin usage (for which the correct classical form would be "nexus" with the "u" long). However, as this heteroclite is used modern legal texts, if you had to mark the vowel (which, as I have said, you would not do in a standard text), yes, the "i" would be long.