For #1, <
Rubylips' solver> spots the following chain ...
r5c9~9~r1c9-9-r1c3-3-r2c1~3~r7c1~2~r5c1-2-r5c9
... so r5c9 cannot be 9, and that seems to do the trick.
Edit: Add the following:For #2, there's a simple reduction based on row-candidates, after preliminary simple moves ...
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2 3 8 | 1 9 7 | 4 5 6
4 5 1 | 68 2 68 | 3 7 9
6 9 7 | 4 5 3 | 2 1 8
----------------+----------------+--------------
8 67 56 | 2 3 1 | 57 9 4
9 2 4 | 7 6 5 | 1 8 3
57 1 3 | 9 8 4 | 57 6 2
----------------+----------------+--------------
17 48 9 | 58 147 2 | 6 3 15
3 67 2 | 56 17 9 | 8 4 15
15 48 56 | 3 14 68 | 9 2 7
There are only three possible candidate-rows for r7:
1-4-9-8-7-2-6-3-5 (a)
7-4-9-8-1-2-6-3-5 (b)
7-8-9-5-4-2-6-3-1 (c)
There are only two possible candidate-rows for r8:
3-7-2-6-1-9-8-4-5 (a)
3-6-2-5-7-9-8-4-1 (b)
The only compatible candidate-rows for r7 & r8 are
r7(b): 7-4-9-8-1-2-6-3-5
r8(b): 3-6-2-5-7-9-8-4-1
and
r7(c): 7-8-9-5-4-2-6-3-1
r8(a): 3-7-2-6-1-9-8-4-5
therefore r7 & r8 reduce to
r7 = 7-48-9-58-14-2-6-3-15
r8 = 3-67-2-56-17-9-8-4-15
and the solution follows with simple moves.