I don't know Java, but my approach to #2 would be generate 2 random integers, lets say from 1 to 100. If both numbers are between:
1-50, win 10euro
51-77, win 20euro
78-92, win 50euro
93-98, win 200euro
99&100, win 1000euro
since the selection of integers from 1-100 is random, it doesn't make any difference statistically that prizes are grouped.
Beginning of #3 would be have a user input values into 5 variables, and check if each is equal to any of the previous between each input.
I'm not quite sure what the question is asking regarding the sum of 10 numbers, since there are only 5 being entered.