The word להשיג is more like "obtain" like you are doing the action of getting something. לקבל is more like "receive" someone else is doing something and you are receiving/getting something from them. It is confusing coming from English where we use "get" all the time.
Obtain and acquire should be acceptable translations, no? It is FAR more specific than "get", as we all know how versatile get is.
Can this also mean "The cat is getting food all morning", or is there a different way of saying that? Duolingo doesn't accept it.
Getting can also mean that the cat recive (מקבל) his food, with no action on his side. משיג means that the cat doing some affort in getting his food
Rrceive means מקבל, when you receive something, you get it for free. When you משיג/ה something you're doing an affort into it
Is it right to use present continuous in the English translation? Everyday suggests an habit, and I would think that the only correct way would be with present simple.
In Hebrew there is no differentiation between present simple and present continuous. There is only one present tense. So either is acceptable when translating to English, there may be some rare cases where by the context one or the other would not be acceptable, but in general it can be translated either way.