According to the FAQ, Healing Medal gadget makes monster less focus. So if I have a Healing medal gadget and a wind drum out on the farm, would the effect of healing medal on that gadget be cancelled out with the effect of the wind drum?

....I know it's late, but I have just realized I have no life while sitting in my room playing PS2 on Independence Day. And to answer you question, yes and no. In my example the Wind Drum is to the Healing Medal Gadget(HMG) what the Egg is to the Chicken. So........

NORMAL TRAINING FOCUS = EXAMPLE MAX 75%
W DRUM TRAINING FOCUS = ADD MAX 25%
HMG LAZYNESS DEFICIT = SUBTRACT MAX 10%
75 + 25 = 100 - 10 = 90
90% = OUR NEW TRAINING AVERAGE(in a perfect game)
Now to check my arithmatic: 90 - 75 = 15
15% = THE AMOUNT OF BOOST WE STILL GET FROM W DRUM DURING HMG LAZINESS.
So no, kind maiden, they do not cancel each other out exactly. Instead, you still end up with a decent boost plus your monster stays happy. But do what the pros do instead: use Wonder Well. It's there for a reason. Heck, use two. And switch your monsters to Lv. 2 Intense ME Gadgets instead (or Lv. 4 IMGs if you're up to that level of skills(but use three Wells)

Where did your math come from, may I ask?

Specifically these two:

W DRUM TRAINING FOCUS = ADD MAX 25%
HMG LAZYNESS DEFICIT = SUBTRACT MAX 10%