How's your tutoring with Scarlett doing?

[Silverobama]

The conversation took place between David and me:

Silver: Hey dude, it's been a while.
David: Yes. How have you been?
Silver: Not bad. Still preparing for my test.
David: You can surely get the score you want.
Silver: Haha. Thanks a lot. By the way, how's your tutoring with Scarlett doing?
David: Not bad.

I referred a student to David to teach. Her name is Scarlett and she wants to learn spoken English from a native speaker.

Is the italic sentence okay?

 

[emsr2d2]

The following/This conversation took place between David and me:

Silver: Hey dude, it's been a while.
David: Yes. How have you been?
Silver: Not bad. Still preparing for my test.
David: You can surely get the score you want.
Silver: Haha. Thanks a lot. By the way, how's your tutoring with Scarlett doing going?
David: Not bad.

I referred a student to David to teach. Her name is Scarlett and she wants to learn spoken English from a native speaker.

Is the italic sentence okay?

We usually ask "How's XXX going?" If you want to use "you" and/or "doing", I'd say "How are you doing with Scarlett?" or "How's Scarlett doing?" Of course, the first of those focuses on David and the other on Scarlett.
David's second line is quite unusual. It's grammatically correct but it sounds extremely formal. I'd expect "I'm sure you'll/you can get the score you want". We tend to use "Surely" at the beginning of an exclamation with a negative connotation:
Surely not!
Surely you're not going to drink that?!