It sounds like you are really concerned about your mother's health. Regarding her warfarin (coumadin) use, this drug does not cause a low platelet count. It can cause bleeding if the drug level gets too high, so with her low platelet count (which can also lead to bleeding), she should be monitored for this.
When some loses weight quickly and has changes in their blood platelets, it can be a sign that their is some kind of hematologic problem going on. It sounds like she is getting checked out by her health care provider, which is good. She may also need to see a hematologist for more work-up. Good luck!