Make the screen to appear again when the screen is off by just touching the screen. Instead of pressing the on/off button
I'm afraid there is no such facility (though it might exist a device which has this, I've not yet heard of). Screen off means screen off.

However, I may be able to offer an alternative: tasker can react on "motion" as well, so you could use a "shake-pattern" as trigger. A profile I could imagine:


Condition: Shake twice (record the shake-pattern)
Task: Turn display on, unlock, bring app to foreground


I'm not sure if "shake patterns" could also be something like "tap the device twice", so you could try that as well. And though Tasker is a payed app (worth every cent!), there's a free, fully functional 7-day-trial available on their homepage.