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"I've been dying to tell you anything you want to hear" refers to how she tells him she only loves him as a friend because she doesn't want to scare him off.
"'Cause that's just who I am this week" refers to how the deep friendship she always feels for him occasionally develops lust alongside it, which always goes away and comes back yet isn't constant (friendship one week, lust the next).
Think about it: You have to care a whole awful lot about somebody to bother writing a song about them.
The part where he tries to cut off his antlers and the girl comes in and stops him could be like, he thinks he has to give in to her urges/experiment/try to be straight to keep the friendship going, but then she stops him because she loves him how he is (and doesn't want romance to mess up the friendship).
Her dad doesn't want her to hang out with the boy, and he even tries to kill him but when the dad is hit by a car his shoes fly off and he has deer feet.
"Lie in the grass, next to the mausoleum" - To "lie" with somebody is often used as a euphemism for sex, and a mausoleum is used for burial.
That said, she is acknowledging that to make any more than a friendship of the situation could very well kill the friendship or come close to it; the "mausoleum" could also represent regret, bitterness, or guilt she would feel if anything came of her feelings and went wrong.