Do we know a priori any rules about the world? 1) Is there any set of rules that human beings or, more generally, other sentient living beings know a priori before any learning process?
In other words, do sentient living beings always were born knowing some causal relations about the world?
For instance, a newborn baby may not know that walking from a high place in direction of an edge may result on him falling due to gravity. Maybe he doesn't even know that he can move its arms and he only learns that after performing fortuitously an impulse that generates such action. Maybe he doesn't even know that he must breath in order to survive and he only learns that after feeling the discomfort and pain caused by the lack of oxygen.
As a disclaimer, I'm excluding here tautological logical syllogisms such as the principle of non contradiction and other axioms of logic. I'm also excluding here any synthetic a priori knowledge that can be derived from these (if you believe in synthetic a priori).
2) In the positive case, how complex can these causal relations be (maybe a measure or an undeniably remarkable complex a priori knowledge)?
I'm particularly interested in a priori knowledge about normative judgements mainly related to social mores.
This is a pretty popular research topic!
One good place to start might be with the work of Spelke, she's all over this.
Try this: https://www.youtube.com/watch?v=nNq_a_wgdgQ

If you prefer written words, this paper is a nice broad overview, although note the 2007 publishing date, there's been a fair bit of work since then.
Spelke, Elizabeth S., and Katherine D. Kinzler. "Core knowledge." Developmental science 10.1 (2007): 89-96.