Angelito,hope this helps!
It changes into juegan because ue is an exchange of (an) in the present form . I hope it helps !!
If you're asking what it means,
the ballet dancer (or just dancer).
The arms.
The sentence seems incomplete. So i woulds think it's La bailarina en los brazos
Derecha is how you say right.
Da la vuelta derecha is how you say "take a right turn"