Is it possible for warfarin to cause diabetic foot ulcers?

No. No. Warfarin can cause something called, "coumadin (warfarin) skin necrosis", which is more likely to happen if you aren't anticoagulated with Heparin / Lovenox before starting coumadin (warfarin). Otherwise, Coumadin (warfarin) does not commonly affect your blood sugar or your diabetes.
No. Diabetes complicated by peripheral artery disease causes foot ulcers.
No. Warfarin may make you bleed more if you have an ulcer but it will not cause an ulcer.
May complicate it. May not be the direct cause but could cause complications if you have one develop at the time you are on the medication.