156473

For Challenge 2, I have came up with one solution

1+2+5=8
4+3+2=9
4+5+1=10

No number has been used more than two times, so I think it is correct

For challenge 1

1+3+4=8
5+2+1=8
3+3+2=8
4+2+2=8

All of these make a score of 8 in different ways