Which adverbials are considered integrated in the sentence

She worked very fast.

Hopefully, she will be waiting

She was waiting hopefully.

She sang as if she was alone.

Cats love playing throught their lives. Similarly, tigers don't lose their willingness to start a game.

Historically speaking, Elisabeth II is one of the most important characters of our times.

Luckily, she arrived in time.

Luckily, she arrived in time.

She politely accepted the proposal.

I highly recommend reading this book.

We went to school on foot.