Yes, it is! :) "Ulifurahi zamani." sounds a little weird to me - just from zamani having been "the longest time"/"early" - also the word used in fairytales "once upon a time" (Hapo kale zamani...) But you might often hear "Nimefurahi sana jana." f.ex. or "Ninafurahi kusikia." (I am glad to hear that.)
Yes, -furahi is a verb (from Arabic) which means to rejoice/be glad/joyful/happy...