How to tell a crater is old or not?
Based on Wikipedia, we can estimate the age of a planet's surface.
How to tell a particular crater is newly formed or not? It may have sharp edge.
Different astronomical objects may have different kinds of environments which may make this more complicated.
Are there any peer-reviewed papers?
One criterion that works well is the presence or absence of smaller craters inside. If the crater is clean, it's probably new. If it's full of smaller craters, it's old. This applies to planets and satellites with no atmosphere, or with a rarefied atmosphere.
This only gives relative age, but no Idea about absolute age. To get this you have to actually go there and get samples.
You could also estimate the rate of bombardment in that place and that would give an indication of the age of the crater