I know how the use of the favor works, my question is because of a debate with friends.
Can you use the Imperial Favor for both of its abilities in the same turn, as it is not a card? Can you use the same ability twice?
Use of the Imperial Favor
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Can you use the Imperial Favor for both of its abilities in the same turn, as it is not a card?
Yes. The two usual abilities that require to discard the Imperial Favor as a cost are player abilities from the rulebook. They do not come from the Imperial Favor itself, they are on each player.
Can you use the same ability twice?
Assuming you mean "twice per turn", no. The default "once per turn" restriction affects all abilities, not only those on cards. See Card Features, Abilities and Abilities and actions, Using abilities.