"Not only does she sing, but also dances" is the term that i came up with. Reason why this is incorrect?
Is there a rule regarding the use of ngảy or máu to mean dance. In another question máu is used for dance?
Duges, I think you mean "nhảy" and "múa" instead of "ngảy" and "màu". But, yes. Múa is for graceful dancing like ballet. Nhảy is for other less graceful dancing. You can remember the difference by remembering that nhảy also means other more active motions like to jump, skip and leap.
The distinction is the target audience. Múa is a dance for an audience (thus, a performance dance). Nhảy is social dancing. People may be watching you (e.g., at the clubs), but you're dancing for yourself and/or with your partners.