I have not voted on any of your questions, and I won't justify the observed downvoting behaviour. I do find the questions as written as problematic for MathOverflow. Even though the posts concern mathematical issues from which good questions can arise, I am not finding your choices that good for this forum.
I focus on one question "Why does this pattern emerge?". As I read the question (and exaggerate some effects for communication), it amounts to saying "I decided to pick a couple of arbitrary operations on sequences, applied this to the prime sequence, and got something I find pretty. Why?".
Why is it pretty? Why did you pick it? Why do the operators do this? It is hard to deal with such a nonspecific question. Better would be to ask: I am studying this operation on sequences. It appears to give this behaviour. Is this operation considered in the literature? Are there related studies that might help me investigate it further? Is this statement phi true? ( phi being a well formulated conjecture on the operation, like ' does OP(Primes)= Famous sequence?'.)
I get the feeling that the questions follow the pattern "Here is an interesting observation. Please continue the research for me." , whereas for MathOverflow it is better to say "Here is an interesting observation, and here is some additional work I've done which suggest the following questions/conjectures. Can some one tell me how I can continue my work, or if it is in the literature, or if there is something I'm missing to go forward on this specific issue?". My impression of the community is that they are willing to help you help yourself more than do the work for you. It might be good for you to preview a question here on meta and ask how you can make it more suitable for the forum.
Gerhard "We All Want Good Questions" Paseman, 2018.07.15.