Carpe Diem, first off, actually means to "pick, or pluck" the day. The ideal of seizing the day is to take each day and pick it out, making it special. Carpe tempum would work in today's world as a cute aphorism, but if you want an exegesis on the Latin, you should go to /r/Latin.

Considering that the previous line from Odes 1:1 states that time has already fled, it would be contextually redundant and a bit nonsensical. In other words, yes if it is for a tattoo surrounded by butterflies; no if it is relating to the literary context of Horace's writings.

This post has been removed as it's not a history question. There are a few latin / translation subs around which could be a good fit.