There are no levels because of the Sphere Grid in X. <_<
Scan Seymour, the description will tell you what order he will attack in, you just need to use the Null spell corresponding to the attack he will do next.
In his second stage, he will attack two different people so he can't kill you if you do it right.
Also you don't need to power up, the entire game can be completed without touching the Sphere Grid or Aeons (the story and Omega Ruins at least, not sure about most of the Dark Aeons, Shinryu or Nemesis).
Wrong.
The game cannot be completed without using the sphere grid because your characters are too weak and cant beat the boss that your up to.
And you cannot advance in the game without using Aeons because there are specific battles where you can use aeons and aeons only.
Anyway, as for Seymour...
His first lot of spells goes in the order of Ice, Lightning, Water then Fire incase you didnt already realise. Lol...
Use Yuna's Nulspells in order every time she has a turn.
As for Anima, i used Auron and Tidus' attacks to kill him before his overdrive charged but my characters were stronger than average when i faced her. Using an aeon could prove helpful, particularly Shiva as she is immune to Anima's "Pain" effect of instand death, and you can use ice spells on yourself to regain full health.