First of all, just to make this clear, you can't
multiclass like Dak'kon does. You
dual-class, that is,
completely switch over to the mage class, losing your fighter skills in the process (including the base to-hit ability, and use of weapons other than the edged type ones).
You do get character points every level, but
not for levels that you "repeat" in another class. Class levels are independent, and you start over when you switch, so you temporarely stop gaining points until your level in your current class goes above your level in your previous/other class(es). In your case, since you're a level 5 fighter, you'll have to reach level 6 as a mage to start getting character points again. But note that the first time you switch to a class, you automatically gain enough experience to immediately reach level 3 in it, just like you started as a level 3 fighter.
(In case it's not clear: class change isn't permanent. You have to train to be a mage - or a thief - to be able to
be that class, but you can choose to go back to the fighter class, then switch to mage again, etc. No limits, it's just a matter of finding a trainer. If you're willing to waste experience points.)
Making the most of the mage class includes getting double-specialized in it, because it'll get you some nice bonuses later. Class specialization bonus is given at levels 7 and 12 for the class that reaches them first; double-specializing means getting both for the same class, so training to be a mage before reaching level 7 as a fighter is recommended.
Your Intelligence is unfortunately quite low - not just for a mage, but for getting a lot of dialogue options (which is more or less the
entire point of being a mage, because this class relies on Intelligence and not on Strength or Dexterity, neither of which affects conversations outside of rare occasions where you, say, catch a pickpocket via dialogue). You can get more from tattoos once you switch, though, I think there's a +2 one a mage can wear. Overall, Intelligence has less effect on dialogue than Wisdom, but it
is quite useful.
Also note that a mage with 19 Intelligence can learn unlimited number of spells, and the highest Intelligence check in conversations is 21. So even with specialization bonuses and tattoos you should aim for natural Intelligence of above 13, and if you ever play again, I suggest starting with 15-16 so you can get more dialogue options early on (nothing too important, but it's an interesting effect). It's not like you'll need a lot of points in your physical stats, with innate health regeneration and mage shield spells and bracelets.
Finally - Dak'kon is not a very efficient spellcaster. His build is that of a melee fighter who relies on spells for support, with 13 Intelligence he can't learn as many spells as a dedicated mage can, and his tattoo slots are better suited for boosting his Strength for more damage. His Circle of Zerthimon spells are quite enough for him (and you can learn some yourself once you're a mage, but you'll need high Intelligence and Wisdom to finish the Circle. Totally worth it, by the way.)