A great place to start is this Frequently Asked Questions list. Then a good place to go next is our in-depth help in developing your department's own system. Email firstname.lastname@example.org for more help.
Whether you are using university resources/funds to reward your employees or giving a non-monetary award, you should always track recognition awards.
There are. Read more about the yearly Service Awards Ceremony here. There is also an Employee of the Month program where employees are selected each month to be honored for their effort and awarded a gift packet from the Chancellor.
That is certainly still allowed. Please understand that you will not be reimbursed for personal investments into your department's recognition awards.
Please email email@example.com to inquire about availability.