what not

I haven't lived there for a year now, because I've been traveling and working and what not.

You can use the phrase 'what not' to show that other similar things can be added to your list, but you don't want to say all of them.  Notice the following:

1. The stores are full of Valentine's Day decorations and what not.
   
2. We will have hamburgers and what not, but if you want anything special, you should bring it.
   

young adults

I'm trained to teach younger children, but recently, I've begun teaching older students, or young adults.

'Young adults' are people from 18 to 30.  Notice the following:

1. A lot of young adults still receive a lot of help from their parents.
   
2. This apartment building has mostly young adults.
   

I have no idea

I have no idea where I would like to live in the future.

You can use the phrase 'I have no idea' when you don't know the answer to a question or you haven't really thought about it. Notice the following:

1. I have no idea where my keys are.  I'm going crazy looking for them.
   
2. I have no idea where we could buy something like that.
   

settle down

I would like to travel to different places and maybe settle down back in Toronto.

'Settling down' usually includes having a reliable job, your own place to live, getting married, and having children.  When you settle down, you commit to living in a particular area.  Notice the following:

1. His parents are always asking him when he's going to settle down.
   
2. They settled down when they were very young.
   

moved to

My parents moved to Vancouver and that's where they live right now.

When you 'move' from one city to another, you are changing the location of where you live.  Notice the following:

1. He just moved to his new apartment last week.
   
2. It was very stressful to move from East Coast to the West Coast.