At the beginning is a melody I’ve heard a thousand times on the piano, but the name escapes me. Something “Arabesque,” maybe?
At 2:27 is a melody that sounds vaguely familiar as well. Any ideas?
And yes, I know that song was used to great effect in Bill & Ted’s Excellent Adventure.
The opening is Rondo Alla Turka (Turkish Rondo) from the 11th Piano Sonata by Mozart. I’m unsure of what the second one is.
It was in the first Fantasia movie by Disney. Argh! It is on the tip of my brain! ETA: Tocatta and Fugue by Bach?!
Yes, that is what it is, start at about three minutes fifty seconds on this clip.
Of course, we can’t overlook the classic of classics at 2:34
Shave and a Haircut. 
S^G
The second one isn’t the Toccata and Fugue, but there is some resemblance. It could be some other piece or just their improvisation.
I thought the latter, although I like to be cautious in these threads, and let others float that possibility first in case they’re wrong 