1) The speaker pleads with his mistress to let him touch her and to lose her virginity to him.
2) She is being coy because they aren't married, and being sexually involved with him would stain her honor as a woman.
3) If they lived for eons, it would be OK for her to put him off. He would use the eons to love her from a distance. But their lives are short. Therefore, she should enjoy physical love with him.
4) Vegetable love wouldn't be physically active like an animal; it would grow in one place instead.
5) "Like amorous birds of prey, rather at once our time devour" describes a fierce, active, physical love.
6) "Roll all our strength and all our sweetness up into one ball" suggests they should be so close they are one.
7) "Deserts of vast eternity" don't contain any physical satisfaction.
8) The sun stands for time. Time will pass and they will die; they have no control over that. This is expressed by "we cannot make our sun stand still".
9) The poet urges her to "carpe diem" or "seize the day".
10) Acting on physical desire means being truly alive for him.