I play a character that does a little spellcasting along with his conventional fighitng. I basically joined the Mages College at Winterhold in order to ger more powerful Destruction spells. They are the same as WinterHaven Court Mage's Spells. Will they be able to sell me better spells only as I master the arts or do I have to tramp around in more dungeons and hope to get a fireball spell from a chest somewhere?

Yes and yes. They only sell them as your level goes up, but you can find higher level spells in chests and whatnot without having the level.

So those spells are not shown or they're there and i cannot buy them?

You would have to ask the coders.