What you can do is perform the sum operation on the AMOUNT value where the DATE is equal to the first DEFAULT_DATE for each CUSTOMER.
Now for getting the number of default customers for each CLASSIFICATION, refer to the code below :
df <- structure(list(CUSTOMER = c(1L, 1L, 1L, 1L, 2L, 2L), LOAN = c(101L,
102L, 103L, 104L, 201L, 202L), DATE = c(201601L, 201603L, 201501L,
201501L, 201601L, 201603L), AMOUNT = c(100L, 100L, 100L, 200L,
100L, 100L), LOAN_DEFAULT = structure(c(2L, 1L, 2L, 1L, 1L, 1L
), .Label = c("N", "Y"), class = "factor"), CUSTOMER_DEFAULT = structure(c(2L,
2L, 2L, 2L, 1L, 1L), .Label = c("N", "Y"), class = "factor"),
DEFAULT_DATE = structure(c(2L, 2L, 2L, 2L, 1L, 1L), .Label = c("-",
"201501"), class = "factor"), CLASSIFICATION = structure(c(2L,
2L, 2L, 2L, 1L, 1L), .Label = c("M", "S"), class = "factor")),
class = "data.frame", row.names = c(NA, -6L))