Translation:In that case, we will eat the food ourselves.
I suppose whomever came up with this (that) sentence would translate "In this case we will eat the food ourselves" to "I dette tilfælde, spiser vi maden selv" to distinguish between "this" and "that". It's still weird and the comma is still not called for. Wouldn't you say that "this" and "that" can be interchangeable depending on context? Anyway there seems to be confusion about it (or this or that) in other language forums: http://english.stackexchange.com/questions/35781/in-non-spatial-contexts-when-should-i-use-this-versus-that
Yes, I suppose there are some contexts where people could pick "this" or "that" and it really wouldn't make a difference, but we don't have further context here and I'd be very wary of a language program that suggested you could just exchange the two words whenever you felt like it.
To be honest I'm finding a lot of instances in the discussion where people want to be allowed a free translation when the meaning can't be guaranteed to be the same, and my own view is that Duolingo shouldn't mark a variation as correct unless the same meaning can be guaranteed.
The comma is not necessary in English, but neither is it wrong to have one. That's a fairly common situation in English (in the past I've worked for one person who inserted commas whenever possible, and another person who inserted commas only when strictly necessary), but I've no idea for Danish.
No. I would accept it. But the Danish sentence does not sound quite natural to me. "I så tilfælde spiser vi maden selv" or simply "så spiser vi maden selv" is better.
There should be no comma, but thankfully Duo Lingo does not pay attention to that sort of stuff. There has been some debate about where to put commas in Danish over the past decades, you may find the latest "rules" here: