Are we only allowed one power?
Yes, but you may receive another through contests/quests/stores.

We sign-up with powers, but our characters aren't allowed to use them... ?
Your character is not permitted to use his/her power until he/she has officially received it from a horse with the Bestowal power. Once you've officially received the power of your choice, your profile will be changed and your character will be able to use the power he/she has chosen.

Is there any way to get around horse bans?

No. Unless a staff member gives you permission, and the staff member can later confirm that, you are not allowed to make banned horses.