1) Suppose my khums date is 31 dec and on that day I have 1000 peny in my hand and I calculated the amount of khums for that amount and after sometime I got some peny from somewhere in terms of earning so will I need to remove khums for that peny also?
2) If I haven't calculated khums on the prescribed date and I received peny in term of earning on that day then will that money included in khums calculation ?

1- Yes, if you earned it before sun sit.
2- Same as 1, except if you mean with (that day) 1st of Jan, for example.