barging here with a few tidbits, don't mind me:
another way they call changyu here is fan jia yatou 樊家丫头: basically means the girl of the fan family
rather than mr. zhao, changyu calls him zhao da shu 大叔: it's a more more affectionate, familiar term to refer to someone's older (who's around the age of one's dad/uncle who is not a direct relative) it's more like her calling him "uncle zhao!"
the underlings using shu xia 属下: it's a subordinate self-referral that they use in front of their superior-- when xie zheng's underling found him rather than "we are late" it's more of "your subordinate(s) is late", same with li huai'an underling when he was giving advice during the talk about the former's arranged marriage, rather than "i think" it's more of a "subordinate thinks", same goes with UILF wei yan's underlings
another one is that magistrate referring to himself as xia guan 下官 when talking to li huai'an, it's also another hierarchical-etiquette thing, he's basically referring to himself as "your humble servant"/ "I (the lower ranking official)" in front of the latter, usually used by lower-ranking officials when addressing superiors/higher rank, or when addressing seniors.
contrast that to when he's referring to himself as ben xian zhun 本县尊 when talking to his subordinate; much like the ben hou explanation above, but rather than "marquis" it's "county magistrate"
xie zheng refers to wei yan as jiu jiu 舅舅 in the flashbacks: uncle, yes, but maternal uncle
much like the explanation for xie zheng's use of "mo" above, he also refers to himself as cao min 草民 (grass people/commoner) it's a self-addressed form when addressing officials/superiors (again he uses it sarcastically/nonchalantly in that exchange with huai'an since changning shows up)
fuqin 父亲 and die 爹: both translated as father which is true, but there is a distinction in terms of colloquiality and to an extent formality- best way i can put it: the former is "father" the latter is "dad" "pa"; how wei xuan refers to wei yan, how changyu refers to her dad, how xie zheng calls her dad and how xie zheng's mum talks to him about his dad and so on and so forth
muqin 母亲 and niang 娘: same as above, but the mother version
general he, during the grave visiting scene with li huai'an, refer to himself as lao gu tou 老骨头: direct translation means old bones, but it's basically a sort of.... humble/self-depreciating reference of "this old man" if i could desc it, it's like "this man who is too old&useless"-- fun fact: in different context it's also used as a nickname when describing an elderly to imply that they're too stubborn (hard-boned) lol.
he also uses the good ol' lao fu 老夫 lit translates to old man: another self-reference term; this one's for elder men
li huai'an on the other hand sometimes refer to himself as xue sheng 学生 when talking to general he; lit translates to learned person/student but this is another self identifying term used by individuals seeking guidance from someone of higher social standing, age, or expertise, basically he refers to him self as this student, your student, when talking to the general
hence why he also call general he lao shi 老师, he doesn't refer to general he as "you" per translation; it's more respectful, in this context: he calls him teacher, his teacher.