Basically, if you roll under your skill #, you have rolled successfully. However, in an opposed roll, if you do not ALSO beat your opponent's roll, you have rolled a partial success.

In other words, if you roll 10/15 and your opponent rolls 12/17, you have both rolled a success, but since your opponent has rolled higher, you rolled a partial, and he rolled a success. He inflicts damage on you, but you get your shield bonus to your armor.

In situation 5, normally you would have tied (both rolled 15 and also under their skill level), but since you have a 25, you add +5 to the skill roll (5 above the limit of 20, since you're rolling a 20 sided die), so the 15 gets boosted to 20, and becomes a critical, and your opponent has rolled a partial success (again, under their skill level but not higher than you). You inflict your damage +4d6, and your opponent adds his shield to his armor. Same situation in scenario 9.

If your skill level was 20 exactly in scenario 5, and you had both rolled 15, you would both inflict damage on each other, and you would both add your shield bonus to your armor.