Adjacent Sums

Place the numbers 1 thru 9 in a 3x3 grid such that every adjacent pair
(excluding diagonals) has a different sum.

Your first solution will not use three possible sums. Repeat #1, using
these sums.

What is the largest possible difference between two adjacent numbers
in the grid? Can you find solutions with this difference
to satisfy #1 and #2 above?
Source: Original.
Solution: An answer to number 3, with the largest difference of 8
(between 1 and 9) can solve 1 and 2:
Solution 1:1 9 7
2 4 8
3 5 6
    
 Solution 2:9 1 3
8 6 2
7 5 4

The first answer doesn't use sums 4, 7, or 17. The second answer (which
is simply the complement of the first  subtract each number from 10)
doesn't use sums 3, 13, or 16.
Carlos Rivera sent this answer
to problem 3 (the unused sums are 4, 6, and 16). Its complement is
also shown (unused sums: 6, 14, 16):
Original:2 1 6
3 9 8
5 4 7
    
 Complement:8 9 4
7 1 2
5 6 7

Putting the 1 in either the corner or the center, with the 9 adjacent,
leads to surprisingly few solutions. Can someone find them all?
(Put the 9 in the top center position for comparative purposes if you
do this.)
Mail to Ken