1. This is correct behaviour to my knowledge.
2. Not sure unfortunately
3. They need to run the test again. Bookmarking is not possible. And to be honest it doesnt sound like a test/exam if they can bookmark and come back. Cheating sounds extremely simple.
In my opinion the test functionality that is delivered through the authoring tool is sub-par and should be avoided if necessary. There are some options.
1. Create a SCORM package as a test/quiz. This will allow bookmarking.
2. Look into tools such as Workforce Performance Builder (SAP tool) or Questionmark (integrated with SAP - this is the "Rolls Royce" of tests)
Remember the test player requires local JAVA installation and correct versions - not good if the test is taken by many people. SAP have also communicated many years ago that the test player functionality will not be developed further.
Hope this helps 
Morten