Yes it does sound like 'veja' and there was another sentence where it also sounded like this. I tried it in google translate, and although the 'D' was softer than pronounced in English is was still recognizably a 'D'. Is this a mistake or do some Spanish speakers pronounce 'D's' like 'V's'?
It is my understanding that the reason why you use "las" IS because it's NOT SPECIFIC food.
I thought this was the best explanation: http://www.spanishdict.com/answers/167561/is-there-a-rule-for-when-you-use-the-definite-article-before-a-noun-me-gusta-comida-mexicana-me-gusta-la-comida-mexicana
Ever thought how this illustrates the old use of 'leave' in English that is similar to 'let' meaning 'allow' - I give you leave to do that.... Appreciate the complexiry and inter-relatedness of language. Seems like you have not encountered llevar if you object to dejar. It is wonderful though how there are no such confusing words with multiple meanings in English are there?
I was looking at dejar's etymology, and it's from Old Spanish lexar (modern alejar), originally from Latin laxāre, the same root as 'lax', 'relax', 'laxative', etc. It means 'to leave to the side', 'to put down', 'to put away', 'to let go'. So it can be used to leave something somewhere, to let go of a habit, to allow (give leave), to drop off, to leave alone, etc. And as you wrote, salir should be used for personal movement away from. (leaving).
Dejar means 'to leave to the side', 'to put down', 'to put away', 'to let go'. While these can be metaphorically extended to 'allow', I haven't seen many examples of this outside of letting someone do something (i.e., giving leave). You can let someone have food, but you can't let food.
The phrase ‘en mi casa’ literally translates to ‘in my house’, but the translation is given with ‘at my house’. Fine, but there is a subtle difference between these two English phrases: if he leaves it at my house, then he might leave it on the porch, but if he leaves it in my house, then this is ruled out.
So which of these best captures the meaning of the Spanish?