Sounds like a loose cam chain, not tappets. Read up on setting the tension. Chain tensioner is supposed to be handled by a spring, but the plunger gets seized with age. Sometimes it needs a little push, but can easily be damaged in the process.
The owl-ish sound has me confused.
White smoke from the breather was a regular occurrence on all my SOHC bikes at startup and even after short rides. Condensation inside the engine can cause that, creating steam as it heats up. If you can go on a hour long highway ride and it’s still there, it might be something else.
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