Welcome to Tacoma ownership!:lol::lol:
Don't worry we all have it!
The engine tapping is caused by the injector timing valve or the fact that our exhaust is thin steel rather than Thick cast steel.
The take off shudder is well documented! Most people develop this shudder after installing a lift.
But if your truck is stock? Then have the dealer replace the drive shaft. That is what is causing your take off shudder.
Again welcome to the club!