Resolution:
When concatenating, the Date field must be formatted explicitly to avoid output changing to a long date format.
Example: {!Check Date}.format("MM/dd/yyyy") + " & " + {!Check Number}
To check multiple picklist values in a ternary condition, use the OR operator:
Example:
({!Payment Method} == "Check" || {!Payment Method} == "Money Order") ? {!Check Date}.format("MM/dd/yyyy") + " & " + {!Check Number} : " "