What's the difference between "await and wait", and in the case of "sleep and asleep"?
What are the verbs that use this structure of putting "a" as a prefix?
 Wait is intransitive, as in Wait here; await is transitive, as in Await instructions. Wait combined with for is synonymous with await, but await is more stilted or literary in tone: Await [Wait for] your mother.
wait, await. The Columbia Guide to Standard American English. 1993
 Sleep can be a verb or a noun:
Verb: She usually sleeps all day.
Noun: I had only 4 hours sleep last night.
 Asleep can be an adverb or an adjective:
Adverb: He fell asleep in class.
Adjective: We were asleep when you called.
 They're generally adjectives, not verbs:
afloat, aware, alike, afraid, alive, alone, ashamedPrefix a-
a reduced form of the Old English preposition on, meaning “on,” “in,” “into,” “to,” “toward,” preserved before a noun in a prepositional phrase, forming a predicate adjective or an adverbial element (afoot; abed; ashore; aside; away), or before an adjective (afar; aloud; alow), as a moribund prefix with a verb (acknowledge), and in archaic and dialectal use before a present participle in -ing (set the bells aringing); and added to a verb stem with the force of a present participle (ablaze; agape; aglow; astride; and originally, awry).
a - Definitions from Dictionary.com-