Yes

Stomach ulcers are an erosion in the lining of the stomach causing a divot or ulcer. If this erodes into a blood vessel it is an emergency. This can cause dark tarry stools, vomiting of blood that looks like coffee grounds, dizziness that is worse with standing or worsening of pain. These are reasons to go to the ER. Strictly follow your doctor’s instructions.

Yes, they can but generally only if they bleed significantly.

Stomach ulcers can be a problem in two instances.
1. If they break through the stomach from acid, it can spill stomach
acid into the belly and cause peritonitis (an infection inside the belly)
2. If the ulcers bleed heavily, one can have a hemorrhage or dangerous
loss of blood. If that occurs, the stool will become black. In that case
it's essential you reach out to your doctor emergently.

Usually, ulcers are simply treated with a variety of medications available to decrease stomach acid and allow the ulcers to heal. TSZMD

Yes, if there is bleeding or perforation.

Any medical condition can easily become an emergency if there is an associated complication. In the case of ulcers, if there is a perforation causing GI bleeding that could easily become an emergency