You are right, these questions can be tricky. Yes, there is an order for project closure activities and they fall under the Close process group of the Integration knowledge area. I suggest you review the PMBOK Guide 5th edition pages 100-104 which outlines the factors involved with that process.

Also be aware that the Project Procurement Management knowledge area includes the Close Procurements Phase. You may want to review that on pages 386-389.

It would be a good idea to get familiar with the various inputs and outputs of this process group as it should help you understand the flow for completing the closures. Hope this helps.

Is there a particular order or sequence that project closure activities (eg: gaining final acceptance, archiving, lessons learned, releasing resources) should be carried out?

I've seen some exam prep questions like 'when do you mark a project as complete?', or 'what should you do next?' --I don't have the exact wordings of the questions and their sources on hand at the moment, but I find these questions a little tricky as the possible answers are mostly activities under close project or phase...