"We need to produce more food."
Translation:Vi behöver tillverka mer mat.
Well, you can't be sure about non-modal verbs, there are different cases with them. Sometimes the att is needed, sometimes you can't have it, and sometimes both ways are possible. So it's only the modal verbs you can be sure about, the others you'll have to learn individually how they work. (I hope I'll get around to write a list about which works how eventually, but it may take me some time).
Would DL have accepted: vi behöver framställa mer mat? I thought of that first but changed it when I checked the suggestions provided. To me -tillverka- is more like producing eg cars, whereas -framställa- seems more appropriate for agriculture, making something from (almost) nothing.
Yes, we don't use att with behöver. att between two verbs is sometimes optional, sometimes required, and in some cases not allowed, so all three cases exist and it varies depending on the first verb. The main tendency is that modal verbs and verbs that are similar to modal verbs don't take att. Here's a link to a little more detailed explanation: https://www.duolingo.com/comment/7075383