You can only graduate one set of Tuvala gear at the end of the season so no, you can't make a set of Tuvala for an alt character. My own recommendation is to make a set of Akum or Lemoria armor for an alt. The pieces are cheap and thus can be used to repair durability during enhancement easily. And with the number of Advice of Valks that PA gives out these days, enhancing an Akum set or a Lemoria set to TRI isn't that difficult. In terms of weapons, I'd do blue mainhand (Liverto) and Awakening then either an AP offhand or even save for a kutum offhand for the alt. And I have, in fact, done exactly this for several alts that became world boss camp alts.

You can make a one time per family PEN Naru > Narchillian check Fughar. the Pen tuvala can only be done 1 time per season, so if you play multiple season you'll have multiple sets of pen tuvala for other characters.gl