Yes, "corps" is a homograph. It can refer to a branch of the military or a group or organization, and it is pronounced the same way but has different meanings.
Is car a homograph
The homograph for "steer" is a noun referring to a male bovine animal, such as a bull or cow.
No
No, "reject" is not a homograph. Homographs are words that are spelled the same but have different meanings and may be pronounced differently.
Have is not a homograph.
Homograph
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obviously, it is homograph.
The homograph for a glass container is "jar," while the homograph for a rattle is "shake."
The homograph of "end" is "end" as in "the end of the movie." The homograph of "ship" is "ship" as in "a container ship." The homograph of "severe" is "severe" as in "a severe storm." The homograph of "harsh" is "harsh" as in "harsh criticism."
Excluding slang, fresh is not a homograph.