I would go with (E)
If we know that p is greater than 2 it leaves us all prime numbers, which are > then 2 (3, 5, 7, 11, 13, etc) So we can not answer the question and this statement alone is insufficient.
If we know that at least one term is sequence S is divisible by p we can be sure that p equals 3, 11, or 1111, etc. (99: 3*3*11; 999: 3*3*3*37). If p=3, then every term in a sequence is divisible by p. However, if p=11 the first term (9) is not divisible by p. Hence, the second statement is insufficient.
It is obvious that together (1) and (2) are insufficient too.
2)
Pick numbers:
For example: 1,2,3,4,5
try (1): 2*1, 2*2, 2*3, 2*4, 2*5 We will get: 4,6,8,10
Every term after the first is equal to the sum of the preceding term and 2. => YES
(2): p-3, etc. : -2,-1,0,1,2
Every term after the first is equal to the sum of the preceding term and 1. => YES
(3) p^2, etc. : 1, 4, 9, 25 => NO
The answer is I and II
3) How many answers are here? I mean Do we have to pick only one or we can pick several?
Pick numbers and do not forget that the numbers are different and they are not in ascending or descending order in a set.
The key here is to know how to find a mean, range and a medium.
I would go with (A), (B) and (E).
Glad if it helps.