In Audacity, is it possible to check how matched my singing is to other's or just melody, such as out of tune, out of rhythm? The other's singing or melody can be a video on youtube. Thanks!
No it isn't; neither is it possible in wavelab or any other piece of software I've come across. Maybe someone out there knows differently?
What you are asking about is the ability of software to detect (sometimes) very subtle changes in pitch. Vocal pitch changes are not uncommon even for the most perfect of singer and it is the human brain that ultimately makes the choice of singer A over singer B and despite all the pitch nuances that may be present (which again I'll state that are really quite impossible for software to rationalize), usually people prefer the voice that sounds nicest or more appropriate.
Audacity, like wavelab (I believe) can tell you the average pitch of a note that is sung but it hasn't got the ability to be a judge.
It's the same story with timing and rhythm.
While not related to Audacity, AutoTune can tell if you are slightly out of tune and even correct for being slightly out of tune, however that is the limit of what I know of for correction. It wouldn't be able to match to a sample if the sample wasn't in tune though I don't think.
Being off rhythm should be pretty obvious without a plugin as one sound would stop before the other if played together.