is it possible for a federal agency with appropriated funds, to create an award.  Such as an "in remembrance" award that the public can apply for and receive?  This is still in the infancy phase but need to provide advice on if it is possible?  Would it follow the rules of a grant? would it be required to be given to a company?  any advice?

What is the deliverable under the resultant contract?  Having some trouble understanding the Government's requirement.

See 31 USC 6303 and 31 USC 6304 to help determine if a contract or grant may be appropriate.

Are you referring to "prizes" when you use the term "award"?  If so, you may want to check out the following:

• https://www.challenge.gov/list/
• 15 U.S.C. Code § 3719: https://www.law.cornell.edu/uscode/text/15/3719 - with respect to your appropriated funds question see paragraph (m)

Based on your question, it appears you have some type of appropriation.  Do you have a statutory authorization to spend those funds on an award?  There is no authority to spend and appropriation without a specific authorization.  What agency are you with?  What color of funds do you have?  What does your agency's authorization act say you may do with those funds?