What do I do with fame points I earn ?
I look at the items and can only buy drake eggs or is there other things ?

Fame can't buy you much at the moment, but there will be a new update in the very near future where nearly everything that you can buy for realm gold, will be available for fame.

Save it for now. Apparently a fame revamp is in the works, which will enable you to purchase just about everything that currently costs gold.
I listened to a little bit of a podcast about it. Iirc, vault slots/character slots will still cost gold, but just about everything else will be purchasable with fame.

My face when this is the only thing worth buying. :L

No kidding. Even if I weren't a poor motherfucker on unemployment I'd still not spend money on this game.
I enjoy playing it because purchasing gold really doesn't help you out very much at all. It's mostly used for aesthetics. And I suppose you can buy health/mana potions with it, but I wouldn't consider that a huge advantage.

I am looking forward to buying dyes/trench & tomb keys and backpacks for fame. :S

This is very very true.