I haven't heard Nelly speaking, but I can bet her accent is not exactly the same as here singing. Many singers in Britain or America (or anywhere else) put on a peculiar accent when they are singing because they think it sounds more romantic or more cool or whatever. For instance, it is easy to notice she doesn't pronounce the R's, though in Canada people do pronounce the R's. She's probably under the influence of American black English and trying to sound cool, or under British influence and trying to sound posh (more poetical).

HONESTLY= We start a sentence with this word to emphasize what we’re going to say. It literally means "I’m going to tell the truth".

WHAT WILL BECOME OF ME?= What will my future be?

WAY TOO CLEAR= Much too clear, too too clear. We can use WAY to emphasize TOO.

DANDY= good, nice.

WHAT= If we find WHAT in a statement (not a question) it usually means "the thing that". The sentence "we are what we don’t see" means that what we see of us is only appearance, our true identity is invisible.

(WE) MISS EVERYTHING= The subject WE is missing, but we know it is the same as the previous sentence. When you miss something you don’t get it, you lose it, you don’t experience it.

DAYDREAMING= Fantasizing (like having a dream but not sleeping). She says that if we live in a fantasy and don’t face reality, we miss all the important things of life. But people think life is horrible, so they prefer to escape reality by daydreaming.

FLAMES TO DUST= An abbreviation of "flames turn to dust", "flames become dust". If something is burning, first you get flames (a good thing, because flames give you light and warmth), but then the good thing finishes and all you get is dust (cold dark dirt).

LOVERS TO FRIENDS= In the same way as flames finally turn to dust, love also cools down, passion dies and lovers become friends. Friendship is good, but if you want to keep the passion, you will not appreciate the friendship that comes later and then love will disappear completely.

WHY DO ALL GOOD THINGS COME TO AN END?= This is the desperate question of someone who still doesn’t understand true reality. A person that only sees death where something new is beginning. The whole song is giving an answer to this question.

EXIT= the way out.

WONDERING= If you wonder, you are curious about something and you want to know.

RESTLESS= Never still (not resting), dissatisfied.

STRESS= To stress is to emphasize, to highlight, to make prominent/important.

LIVING THIS WAY I STRESS LESS= She says that if she’s only noticing exits (the end of things) and wanting to stay young and restless, she will miss the important things of life, the highlights.

PULL AWAY= To withdraw, to retreat, to move away, to leave.

THE PAIN SETS IN= When something sets in, it begins to happen.
- The night finally set in and everything turned black.

I ONLY FEEL GRAVITY= Gravity is a force that pulls you down to earth, so poetically, to feel gravity is to feel sad.

I WONDER WHY= I don’t know why and I want to know. When you wonder /wʌndə*/ you don't understand something, but would like to know. 

WHISTLING= /wɪslɪŋ/ The verb to whistle is pronounced /wɪsəl/, the T is silent. To whistle is to produce a sound or a melody by forcing air out through your rounded lips.

TUNE= /tju:n/ Melody, music. An assimilation rule says that T+Y=CH, so this word is usually pronounced /tʃu:n/ in modern English (both BrE and AmE)

BARK= People speak, cats meow and dogs bark. To bark at the new moon is to bark in that direction, as if the moon were listening to them.

The figure of the dogs barking at the new moon is poetical and obscure (not clear to understand). The new moon is the phase of the moon when it is invisible (completely dark), so it is part of the cycle where the moon is "dead". But at the same time, we call it "new moon" because it is the beginning of a new cycle. A dog or a wolf barking at the moon is usually an image of death, fear, sadness. But these dogs are not sad, they are not "crying" (howling), they are "whistling a new tune", singing something new, so it is a happy thing and it means change. They want the next cycle of the moon to come (hoping it would come soon) because they want to die... and start again, changed, like the moon, always the same, always changing, growing, whining and dying... only to be born again.

Yeah, I know, I’m going a bit over the top (too expressive or dramatic), but that’s poetry!