Something is not right. I am not that up on your MY. But timing sounds like an issue or vacuumn maybe fuel. You also have less significant issues to deal with.
Someone may jump in with a little guidance. Check your timing, vacuum lines, fuel distribution, compression. You indicate a timing belt refresh; if these engine behaviors happened after that check your cam configurations first. Hopefully a configuration issue and not a failure in the valve train.
I hope you are a gearhead
