My specific question is, why is not any auxiliary followed by coming?
I've seen a lot of sentences as following one, but this time it made me wonder if there was any grammar behind that like omission or participle clause, or it was just an informal spoken English.
You feel another one coming?
I thought it could stand for 'Do you feel that another one is coming' or '... that another one comes' or '... that another one is going to come' or '... that another one will come'.
In this sentence one refers to a bird, but I don't think this makes any difference.
Here is another example:
Doctor to a pregnant woman: "(Do) You feel another one coming?" (one refers to contraction)
How about this example:
(Do) You think he (or him) coming?