I made this comment in the website but don't know how it was removed. I can't put same comment there now. So putting the comment here:

First case:
It is difficult to reach the diagnosis following a single episode of blood vomiting due to acute upper gastrointestinal bleeding which is medically known as hematemesis, without knowing prior medical history or examining the patient. But we can think about some differential diagnosis. According to the frequency rate of hematemesis, most important diagnosis is bleeding peptic ulcer. Gastric erosion is second diagnosis. Both of the cases, use of NSAIDs and ingestion of alcohol are considered as causative factor. We need to enquire about it. If Rose’s grandmother is suffering from any liver disease manifested by jaundice, ascites (collection of excess fluid in abdominal cavity), enlargement of liver and spleen etc. rupture of esophageal varices is a fearing diagnosis here. Considering her age, cancer of stomach or esophagus might be a cause. Or, simply, due to “not feeling well this week”, if she did severe retching (try to vomit up but can’t), this type of blood vomiting may happen due to tear in the lower end of food passage (Mallory-Weiss tear). The last is not usually dangerous one, and self-limiting.
Regarding management, a patient with hematemesis should always be treated in a specialized unit of a hospital. So take grandmother to the nearest health facility ASAP. Doctor will assess the patient clinically, and resuscitate. Putting a large-bore cannula should be the first step. Actions have to be taken according to the ongoing bleeding status (stopped or still bleeding) and effects of the bleeding. If the patient is cold and sweating and agitated, these are not good signs.

Second case:
One sided facial nerve palsy (Bell’s palsy). He is also having dysarthria (poorly articulated or slurred speech). These may be single, isolated nerve problem along with problems in the muscle of speech. But these may be initial signs of cerebrovascular accident (CVA) or stroke. He should be examined by a doctor (physical examination is sufficient enough for the diagnosis of Bell’s palsy). Investigations should be done to find out the risk factors (Hypertension, diabetes, dyslipidemia etc.). Imaging of brain should be done to confirm stroke or CVA.