Shrinking faster than any other nation’s, the projected decline of Jap

If you look up "with" in any comprehensive English dictionary, you'll see it has at least a dozen different meanings. This is true of most simple English words. So it's going to be a hopeless task if you want to try to learn absolute rules about how these simple words can be used - there will be as many exceptions to such "rules" as there are examples that follow them. Often "with" means one thing accompanies another. Often it means something else. In the "starfish" sentence you quote, the first "with" means something like "having" or "accompanied by", and the second "with" means something else -- it's used as an indicator of how something is accomplished.