Both etymonline and wiktionary provide useful comparisons of the several words you ask about. For example, see etymonline's entries for reward, award, prize, apprise, appraise, price, praise, etc. A note in the praise entry comments, “Now a verb in most Germanic languages (Ger. preis, Dan. pris, etc.), but only in English is it differentiated in form from cognate price.” A note in the price entry comments,
Praise, price, and prize began to diverge in Old French, with praise emerging in Middle English by early 14c. and prize being evident by late 1500s with the rise of the -z- spelling. Having shed the extra Old French and Middle English senses, the word now again has the base sense of the Latin original.
Note that prize has two separate etymologies for its different meanings as (1) a noun meaning “a taking, capture, ... a thing seized, ... booty” or plunder and (2) a verb meaning “To consider something highly valuable” or “To move with a lever; to force up or open; to prise or pry”. The noun derives via Middle English and Old French from Latin prendere (“to take, seize”); the verb from Latin pretium (“price, value”), again via Middle English and Old French.