The only Swedish grammar book we have in my town library is from 1977, is there anything I should watch out for?
Probably too late for you to read this, but perhaps someone else is in a similar situation. That time is about when I went to school, and I can only recall two things that have changed, and neither will actually make any difference to the "result".
The verb form now called "preteritum" was back then called "imperfekt", but the form itself has not changed. And I don't know if this change is even visible if the book is not written in Swedish.
People are now taught two genders, common (en-words) and neuter (ett-words). Back then we were taught four, neuter is the same, but the en-words was divided info feminine, masculine and "reale". Basically the former two are used for persons and animals, "reale" for objects. However, since there aren't (nor was) any actual difference* in the grammar between those three, all en-words are joined into the common gender ("utrum" in grammar-Swedish).
(*The adjective ending -e for masculine words still exists, however (at least today, I don't remember what I learned in school) the normal -a ending can be used on all forms, also masculine. There are also some words with only -e ending for any gender.)
Then there are some new words (the gender neutral personal pronoun "hen" for example), and some things considered very colloquial back then might be more accepted today, though such distinction often depends on the person one speaks too, and what they once learned. Also today the letter "W" is just another letter, it might be described different in that book. Altogether, no big changes (as far as I know).
In Swedish does one have to specify what is being cooked (in this case mat)? Is it incorrect to say "Han lagar medan vi sover"?
Can I say Han lagar fisken medan vi sover instead of Han lagar mat medan vi sover?
No, not really. It's not an accepted answer for obvious reasons, but as a standalone sentence it would feel more natural to say "han tillagar fisken..."
Does 'mat' follow 'lagar' in every instance where the food is unspecified in Swedish?
I'd say there is one common exception. If you see someone by the stove, it is common to ask "Vad lagar du?" for "What are you cooking?". However, without context, that same question means "What are you repairing?". When the context is not clear, one need to ask for example "Vad lagar du för mat?" (~ What kind of food are you cooking?).
Yes, laga on its own doesn't refer to cooking. You need to specify.
Tack! Every time you reply to me I feel like a kid again because your profile picture is Pengu and I absolutely adored that show when I was super young, thanks for the memories :)
This reminds me of an ad for a bread company when I was a child. Their tag line was "Baked while you sleep". Many years later, in college a young man I know added on, "I get baked, then I sleep." (it as circa 1970-71 so it was still the '60s. :-))
I'm a little embarrassed to admit that my first thought was "so the modern equivalent for this sentence would be to 'cook meth' then".
would 'he cooks food whilst we sleep' be accepted or is whilst a completely different word?
Why is "He fixes food while we sleep" incorrect? (Most of the people with whom I talk about food use "fix" more often than "cook," as in "What are you fixing for dinner?")
I'd go with fixa for that in Swedish. I mean, you could fix food that doesn't require cooking. :)