The answer is indeed
1. allusion
2. pun
3. simile
4. oxymoron
5. alliteration
6. metaphor
I'll add some more information to why that answer is correct.
The sentence "The date is out of such prolixity: We'll have no Cupid hoodwink'd with a scarf," is an allusion because it refers to a character of literary significance. In this case, the character is the mythological being, Cupid. An allusion does not offer details or a description of such character.
The sentence "Ay, the heads of the maids, or their maidenheads" is a pun because it uses similar words in order to make a joke. A pun can use words that sound similar but have different meanings - which is the case here - or words that offer more than one possible meaning.
"Go ask his name: if he be married. My grave is like to be my wedding bed." is a simile because it makes a comparison. It differs from the metaphor because a metaphor does not use the words "like" or "as".
"O heavy lightness! serious vanity! Mis-shapen chaos of well-seeming forms!" is an oxymoron because it places words that have opposite meanings together. We would assume that, if something is light, it cannot be heavy.
An alliteration is the repetition of sounds or letters at the beginning of words that are close to each other in a structure. We can notice such repetition in "From forth the fatal loins of these two foes- A pair of star-cross'd lovers take their life".
Finally, the sentence "my lips, two blushing pilgrims, ready stand To smooth that rough touch with a tender kiss" is a metaphor because it compares the lips to pilgrims without the use of words such as "like" or "as".
