Well... sütemény has a wider meaning than just "cake". Basically, almost any baked good can be called sütemény - cakes, bars, cookies, pastries (such as the delightfully named apácafing), even some salty or savory things like pretzels or pogácsa. And of course süti is just a cute diminutive version of sütemény.
But torta is much more specifically a cake (usually a multi-layered one).
The children do not eat the cake. but the verb is in singular.... why? i don't understand
The verb is 3rd person plural, definite form. The singular form would be nem eszi meg.
I still don't get how and when to use this meg affix.. could someone give an explanation?
Meg is a verbal prefix that doesn't have a very clear meaning, but mostly means that something is done to its completion:
- ért - to understand; megért - to comprehend, fully grasp
- mos - to wash; megmos - to cleanse (by washing)
- eszik - to eat; megeszik - to finish eating something, to eat it all
Meg is also used to give the action a perfective meaning, like with all other verbal prefixes.