Will the customs inspectors in the United States take my apple cake from Vienna because it has fruit in it or are they only after raw fruit? Also, can I even bring it on board with me these days and shove it under my seat or is that forbidden as well?

I have brought baked goods into the US from Europe many times without ever having a problem. You need to declare it on the customs form where it asks are you carrying any food items. Tell them you're carrying a cake.

It's raw fruit that is the concern due to possible pests.

US Customs are only concerned about fresh fruit/veggies. I brought several cakes and cookies back last December from Vienna. List the cake under the question about food. You should be fine.

Cooked fruit in pastries is fine. They're concerned about fresh fruit which can carry small insects - not desserts.

ditto

No problem with taking it home because--as others have noted--your item has cooked fruit in it, not raw.

As to bringing it on-board in its container, hmmm...maybe, maybe not. Many airports have banned things like Christmas stollen from carry-on because the marzipan filling could be considered a liquid. Ditto for Nutella spread and similar items. So if the cake has any kind of creamy filling, it might be best to put it in your checked luggage.

Thanks for the advice on this. I will definitely make room for it in the suitcase!