With Lullmage Mentor's ability:
Tap seven untapped Merfolk you control: Counter target spell.
Can I attempt to tap less than 7 creatures with his second ability? I know it would not activate his second ability, but can I at least make the attempt to tap 7?
Basically can I intentionally fail to tap 7 creatures and those creatures still get tapped?
No you can't. due to rule 117.3
117.3. A player can’t pay a cost unless he or she has the necessary resources to pay it fully. For example, a player with only 1 life can’t pay a cost of 2 life, and a permanent that’s already tapped can’t be tapped to pay a cost. See rule 202, “Mana Cost and Color,” and rule 602, “Activating Activated Abilities”
the text: "tap 7 merfolk" is before the :, and therefore it's a cost. You can't pay or attempt to pay that cost unless you are able to pay it fully.
